Best Known (95, 95+20, s)-Nets in Base 2
(95, 95+20, 320)-Net over F2 — Constructive and digital
Digital (95, 115, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 23, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
(95, 95+20, 695)-Net over F2 — Digital
Digital (95, 115, 695)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2115, 695, F2, 2, 20) (dual of [(695, 2), 1275, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2115, 1032, F2, 2, 20) (dual of [(1032, 2), 1949, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2115, 2064, F2, 20) (dual of [2064, 1949, 21]-code), using
- 1 times truncation [i] based on linear OA(2116, 2065, F2, 21) (dual of [2065, 1949, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(289, 2049, F2, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,10]) ⊂ C([0,8]) [i] based on
- 1 times truncation [i] based on linear OA(2116, 2065, F2, 21) (dual of [2065, 1949, 22]-code), using
- OOA 2-folding [i] based on linear OA(2115, 2064, F2, 20) (dual of [2064, 1949, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(2115, 1032, F2, 2, 20) (dual of [(1032, 2), 1949, 21]-NRT-code), using
(95, 95+20, 13102)-Net in Base 2 — Upper bound on s
There is no (95, 115, 13103)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 41566 678417 513087 036460 999631 263529 > 2115 [i]