Best Known (39−6, 39, s)-Nets in Base 2
(39−6, 39, 4094)-Net over F2 — Constructive and digital
Digital (33, 39, 4094)-net over F2, using
- 21 times duplication [i] based on digital (32, 38, 4094)-net over F2, using
- net defined by OOA [i] based on linear OOA(238, 4094, F2, 6, 6) (dual of [(4094, 6), 24526, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(238, 4095, F2, 3, 6) (dual of [(4095, 3), 12247, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(238, 4095, F2, 3, 6) (dual of [(4095, 3), 12247, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(238, 4094, F2, 6, 6) (dual of [(4094, 6), 24526, 7]-NRT-code), using
(39−6, 39, 4096)-Net over F2 — Digital
Digital (33, 39, 4096)-net over F2, using
- net defined by OOA [i] based on linear OOA(239, 4096, F2, 6, 6) (dual of [(4096, 6), 24537, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(239, 4096, F2, 5, 6) (dual of [(4096, 5), 20441, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(239, 4096, F2, 2, 6) (dual of [(4096, 2), 8153, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(237, 4095, F2, 2, 6) (dual of [(4095, 2), 8153, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(239, 4096, F2, 2, 6) (dual of [(4096, 2), 8153, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(239, 4096, F2, 5, 6) (dual of [(4096, 5), 20441, 7]-NRT-code), using
(39−6, 39, 14881)-Net in Base 2 — Upper bound on s
There is no (33, 39, 14882)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 549772 175940 > 239 [i]