Best Known (97, 97+20, s)-Nets in Base 2
(97, 97+20, 320)-Net over F2 — Constructive and digital
Digital (97, 117, 320)-net over F2, using
- 22 times duplication [i] based on 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
- trace code for nets [i] based on digital (3, 23, 64)-net over F32, using
(97, 97+20, 756)-Net over F2 — Digital
Digital (97, 117, 756)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, 756, F2, 2, 20) (dual of [(756, 2), 1395, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2117, 1038, F2, 2, 20) (dual of [(1038, 2), 1959, 21]-NRT-code), using
- strength reduction [i] based on linear OOA(2117, 1038, F2, 2, 21) (dual of [(1038, 2), 1959, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2117, 2076, F2, 21) (dual of [2076, 1959, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 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(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- OOA 2-folding [i] based on linear OA(2117, 2076, F2, 21) (dual of [2076, 1959, 22]-code), using
- strength reduction [i] based on linear OOA(2117, 1038, F2, 2, 21) (dual of [(1038, 2), 1959, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2117, 1038, F2, 2, 20) (dual of [(1038, 2), 1959, 21]-NRT-code), using
(97, 97+20, 15052)-Net in Base 2 — Upper bound on s
There is no (97, 117, 15053)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 166206 180334 397712 970657 957304 644494 > 2117 [i]