Best Known (56−14, 56, s)-Nets in Base 2
(56−14, 56, 80)-Net over F2 — Constructive and digital
Digital (42, 56, 80)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (11, 18, 41)-net over F2, using
- digital (24, 38, 40)-net over F2, using
- 2 times m-reduction [i] based on digital (24, 40, 40)-net over F2, using
(56−14, 56, 128)-Net over F2 — Digital
Digital (42, 56, 128)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(256, 128, F2, 2, 14) (dual of [(128, 2), 200, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256, 256, F2, 14) (dual of [256, 200, 15]-code), using
- a “Gp†code from Brouwer’s database [i]
- OOA 2-folding [i] based on linear OA(256, 256, F2, 14) (dual of [256, 200, 15]-code), using
(56−14, 56, 855)-Net in Base 2 — Upper bound on s
There is no (42, 56, 856)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 72446 482858 511627 > 256 [i]