Best Known (31, 31+7, s)-Nets in Base 2
(31, 31+7, 4094)-Net over F2 — Constructive and digital
Digital (31, 38, 4094)-net over F2, using
- net defined by OOA [i] based on linear OOA(238, 4094, F2, 7, 7) (dual of [(4094, 7), 28620, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
(31, 31+7, 4095)-Net over F2 — Digital
Digital (31, 38, 4095)-net over F2, using
- net defined by OOA [i] based on linear OOA(238, 4095, F2, 7, 7) (dual of [(4095, 7), 28627, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(238, 4095, F2, 6, 7) (dual of [(4095, 6), 24532, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(238, 4095, F2, 6, 7) (dual of [(4095, 6), 24532, 8]-NRT-code), using
(31, 31+7, 9373)-Net in Base 2 — Upper bound on s
There is no (31, 38, 9374)-net in base 2, because
- 1 times m-reduction [i] would yield (31, 37, 9374)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 137460 949998 > 237 [i]