# Max SYNC_COMMITTEE_REWARD

According to [compute_sync_committee_inclusion_reward](https://github.com/ethereum/consensus-specs/blob/daf6a0af45753442cd9fefd466dde709e70a829f/tests/core/pyspec/eth2spec/test/helpers/sync_committee.py#L47):

def compute_sync_committee_inclusion_reward(spec, state):
    total_active_increments = spec.get_total_active_balance(state) // spec.EFFECTIVE_BALANCE_INCREMENT
    
    total_base_rewards = spec.get_base_reward_per_increment(state) * total_active_increments
    
    max_participant_rewards = (total_base_rewards * spec.SYNC_REWARD_WEIGHT // spec.WEIGHT_DENOMINATOR // spec.SLOTS_PER_EPOCH)
                               
    return max_participant_rewards // spec.SYNC_COMMITTEE_SIZE

where

base_reward_per_increment = EFFECTIVE_BALANCE_INCREMENT * BASE_REWARD_FACTOR // sqrt(total_active_balance)

EFFECTIVE_BALANCE_INCREMENT = 1 000 000 000
BASE_REWARD_FACTOR = 64

Hence:

total_active_increments = total_active_balance / EFFECTIVE_BALANCE_INCREMENT

total_base_rewards = (EFFECTIVE_BALANCE_INCREMENT * BASE_REWARD_FACTOR / sqrt(total_active_balance)) * (total_active_balance / EFFECTIVE_BALANCE_INCREMENT)

total_base_rewards = (EFFECTIVE_BALANCE_INCREMENT * BASE_REWARD_FACTOR * total_active_balance) / (sqrt(total_active_balance) * EFFECTIVE_BALANCE_INCREMENT)


total_base_rewards = BASE_REWARD_FACTOR * sqrt(total_active_balance)

Using the results above:

max_participant_rewards = BASE_REWARD_FACTOR * sqrt(total_active_balance) * SYNC_REWARD_WEIGHT / (WEIGHT_DENOMINATOR * SLOTS_PER_EPOCH)

SYNC_REWARD_WEIGHT = 2
WEIGHT_DENOMINATOR = 64
SLOTS_PER_EPOCH = 32
BASE_REWARD_FACTOR = 64

max_participant_rewards = 64 * 2 / (64 * 32) * sqrt(total_active_balance)

max_participant_rewards = sqrt(total_active_balance) / 16

max_reward_per_participant = max_participant_rewards / SYNC_COMMITTEE_SIZE

SYNC_COMMITTEE_SIZE = 512

max_reward_per_participant = sqrt(total_active_balance) / 8192

Given the duration of the SYNC_COMMITTEE of 256 epochs = 8192 slots:

max_reward_per_participant_total = max_reward_per_participant * 8192
max_reward_per_participant_total = sqrt(total_active_balance) * 8192 / 8192
max_reward_per_participant_total = sqrt(total_active_balance)

Hence, we have the following max rewards:

total_active_balance = 30 000 000 * 10^9
max_reward_per_participant_total ~ 180 000 000 Gwei

total_active_balance = 45 000 000 * 10^9
max_reward_per_participant_total ~ 212 000 000 Gwei