Best Known (177, 177+30, s)-Nets in Base 2
(177, 177+30, 624)-Net over F2 — Constructive and digital
Digital (177, 207, 624)-net over F2, using
- 23 times duplication [i] based on digital (174, 204, 624)-net over F2, using
- t-expansion [i] based on digital (173, 204, 624)-net over F2, using
- trace code for nets [i] based on digital (3, 34, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 34, 104)-net over F64, using
- t-expansion [i] based on digital (173, 204, 624)-net over F2, using
(177, 177+30, 2390)-Net over F2 — Digital
Digital (177, 207, 2390)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2207, 2390, F2, 3, 30) (dual of [(2390, 3), 6963, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2207, 2746, F2, 3, 30) (dual of [(2746, 3), 8031, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2207, 8238, F2, 30) (dual of [8238, 8031, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, 8239, F2, 30) (dual of [8239, 8032, 31]-code), using
- 1 times truncation [i] based on linear OA(2208, 8240, F2, 31) (dual of [8240, 8032, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2208, 8240, F2, 31) (dual of [8240, 8032, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, 8239, F2, 30) (dual of [8239, 8032, 31]-code), using
- OOA 3-folding [i] based on linear OA(2207, 8238, F2, 30) (dual of [8238, 8031, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2207, 2746, F2, 3, 30) (dual of [(2746, 3), 8031, 31]-NRT-code), using
(177, 177+30, 91595)-Net in Base 2 — Upper bound on s
There is no (177, 207, 91596)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 205 689595 251762 954061 605434 485754 553026 536016 719244 430473 011296 > 2207 [i]