Best Known (185, 185+40, s)-Nets in Base 2
(185, 185+40, 380)-Net over F2 — Constructive and digital
Digital (185, 225, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 45, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
(185, 185+40, 903)-Net over F2 — Digital
Digital (185, 225, 903)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2225, 903, F2, 2, 40) (dual of [(903, 2), 1581, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2225, 1032, F2, 2, 40) (dual of [(1032, 2), 1839, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2225, 2064, F2, 40) (dual of [2064, 1839, 41]-code), using
- 1 times truncation [i] based on linear OA(2226, 2065, F2, 41) (dual of [2065, 1839, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,18]) [i] based on
- linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(2199, 2049, F2, 37) (dual of [2049, 1850, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- construction X applied to C([0,20]) ⊂ C([0,18]) [i] based on
- 1 times truncation [i] based on linear OA(2226, 2065, F2, 41) (dual of [2065, 1839, 42]-code), using
- OOA 2-folding [i] based on linear OA(2225, 2064, F2, 40) (dual of [2064, 1839, 41]-code), using
- discarding factors / shortening the dual code based on linear OOA(2225, 1032, F2, 2, 40) (dual of [(1032, 2), 1839, 41]-NRT-code), using
(185, 185+40, 20195)-Net in Base 2 — Upper bound on s
There is no (185, 225, 20196)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 53 932717 453734 474010 939750 869412 928046 603844 272782 549201 463614 116456 > 2225 [i]