Best Known (96, 120, s)-Nets in Base 2
(96, 120, 260)-Net over F2 — Constructive and digital
Digital (96, 120, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 30, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(96, 120, 397)-Net over F2 — Digital
Digital (96, 120, 397)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2120, 397, F2, 2, 24) (dual of [(397, 2), 674, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2120, 512, F2, 2, 24) (dual of [(512, 2), 904, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2120, 1024, F2, 24) (dual of [1024, 904, 25]-code), using
- 1 times truncation [i] based on linear OA(2121, 1025, F2, 25) (dual of [1025, 904, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2121, 1025, F2, 25) (dual of [1025, 904, 26]-code), using
- OOA 2-folding [i] based on linear OA(2120, 1024, F2, 24) (dual of [1024, 904, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(2120, 512, F2, 2, 24) (dual of [(512, 2), 904, 25]-NRT-code), using
(96, 120, 5398)-Net in Base 2 — Upper bound on s
There is no (96, 120, 5399)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 331262 021354 596428 550472 257154 824614 > 2120 [i]