Best Known (140, 176, s)-Nets in Base 2
(140, 176, 260)-Net over F2 — Constructive and digital
Digital (140, 176, 260)-net over F2, using
- t-expansion [i] based on digital (138, 176, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 44, 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
- trace code for nets [i] based on digital (6, 44, 65)-net over F16, using
(140, 176, 463)-Net over F2 — Digital
Digital (140, 176, 463)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2176, 463, F2, 2, 36) (dual of [(463, 2), 750, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 517, F2, 2, 36) (dual of [(517, 2), 858, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2176, 1034, F2, 36) (dual of [1034, 858, 37]-code), using
- 1 times truncation [i] based on linear OA(2177, 1035, F2, 37) (dual of [1035, 858, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(2176, 1024, F2, 37) (dual of [1024, 848, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2166, 1024, F2, 35) (dual of [1024, 858, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(2177, 1035, F2, 37) (dual of [1035, 858, 38]-code), using
- OOA 2-folding [i] based on linear OA(2176, 1034, F2, 36) (dual of [1034, 858, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 517, F2, 2, 36) (dual of [(517, 2), 858, 37]-NRT-code), using
(140, 176, 6603)-Net in Base 2 — Upper bound on s
There is no (140, 176, 6604)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 95815 403986 678865 139974 020309 652449 785823 646069 314004 > 2176 [i]