Best Known (152, 152+30, s)-Nets in Base 2
(152, 152+30, 390)-Net over F2 — Constructive and digital
Digital (152, 182, 390)-net over F2, using
- 22 times duplication [i] based on digital (150, 180, 390)-net over F2, using
- trace code for nets [i] based on digital (0, 30, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 30, 65)-net over F64, using
(152, 152+30, 1209)-Net over F2 — Digital
Digital (152, 182, 1209)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2182, 1209, F2, 3, 30) (dual of [(1209, 3), 3445, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2182, 1369, F2, 3, 30) (dual of [(1369, 3), 3925, 31]-NRT-code), using
- strength reduction [i] based on linear OOA(2182, 1369, F2, 3, 31) (dual of [(1369, 3), 3925, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2182, 4107, F2, 31) (dual of [4107, 3925, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- OOA 3-folding [i] based on linear OA(2182, 4107, F2, 31) (dual of [4107, 3925, 32]-code), using
- strength reduction [i] based on linear OOA(2182, 1369, F2, 3, 31) (dual of [(1369, 3), 3925, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2182, 1369, F2, 3, 30) (dual of [(1369, 3), 3925, 31]-NRT-code), using
(152, 152+30, 28835)-Net in Base 2 — Upper bound on s
There is no (152, 182, 28836)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 130446 546846 786089 077054 774459 771311 505166 436300 813928 > 2182 [i]