Best Known (129, 156, s)-Nets in Base 2
(129, 156, 320)-Net over F2 — Constructive and digital
Digital (129, 156, 320)-net over F2, using
- 21 times duplication [i] based on digital (128, 155, 320)-net over F2, using
- t-expansion [i] based on digital (127, 155, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 31, 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, 31, 64)-net over F32, using
- t-expansion [i] based on digital (127, 155, 320)-net over F2, using
(129, 156, 803)-Net over F2 — Digital
Digital (129, 156, 803)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2156, 803, F2, 2, 27) (dual of [(803, 2), 1450, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2156, 1046, F2, 2, 27) (dual of [(1046, 2), 1936, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2156, 2092, F2, 27) (dual of [2092, 1936, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2156, 2093, F2, 27) (dual of [2093, 1937, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2156, 2093, F2, 27) (dual of [2093, 1937, 28]-code), using
- OOA 2-folding [i] based on linear OA(2156, 2092, F2, 27) (dual of [2092, 1936, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2156, 1046, F2, 2, 27) (dual of [(1046, 2), 1936, 28]-NRT-code), using
(129, 156, 21990)-Net in Base 2 — Upper bound on s
There is no (129, 156, 21991)-net in base 2, because
- 1 times m-reduction [i] would yield (129, 155, 21991)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 45685 495338 966421 131470 663651 659337 595587 707632 > 2155 [i]