Best Known (185−30, 185, s)-Nets in Base 2
(185−30, 185, 490)-Net over F2 — Constructive and digital
Digital (155, 185, 490)-net over F2, using
- trace code for nets [i] based on digital (7, 37, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
(185−30, 185, 1313)-Net over F2 — Digital
Digital (155, 185, 1313)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2185, 1313, F2, 3, 30) (dual of [(1313, 3), 3754, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2185, 1370, F2, 3, 30) (dual of [(1370, 3), 3925, 31]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2183, 1370, F2, 3, 30) (dual of [(1370, 3), 3927, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2183, 4110, F2, 30) (dual of [4110, 3927, 31]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2181, 4108, F2, 30) (dual of [4108, 3927, 31]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2181, 4108, F2, 30) (dual of [4108, 3927, 31]-code), using
- OOA 3-folding [i] based on linear OA(2183, 4110, F2, 30) (dual of [4110, 3927, 31]-code), using
- 22 times duplication [i] based on linear OOA(2183, 1370, F2, 3, 30) (dual of [(1370, 3), 3927, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2185, 1370, F2, 3, 30) (dual of [(1370, 3), 3925, 31]-NRT-code), using
(185−30, 185, 33126)-Net in Base 2 — Upper bound on s
There is no (155, 185, 33127)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 49 040576 157195 509418 406497 412485 156432 175508 987961 559528 > 2185 [i]