Best Known (151, 190, s)-Nets in Base 4
(151, 190, 1061)-Net over F4 — Constructive and digital
Digital (151, 190, 1061)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 34, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (117, 156, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 39, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 39, 257)-net over F256, using
- digital (15, 34, 33)-net over F4, using
(151, 190, 5148)-Net over F4 — Digital
Digital (151, 190, 5148)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4190, 5148, F4, 39) (dual of [5148, 4958, 40]-code), using
- 1031 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 40 times 0, 1, 65 times 0, 1, 93 times 0, 1, 122 times 0, 1, 144 times 0, 1, 160 times 0, 1, 172 times 0, 1, 180 times 0) [i] based on linear OA(4175, 4102, F4, 39) (dual of [4102, 3927, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- 1031 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 40 times 0, 1, 65 times 0, 1, 93 times 0, 1, 122 times 0, 1, 144 times 0, 1, 160 times 0, 1, 172 times 0, 1, 180 times 0) [i] based on linear OA(4175, 4102, F4, 39) (dual of [4102, 3927, 40]-code), using
(151, 190, 2576346)-Net in Base 4 — Upper bound on s
There is no (151, 190, 2576347)-net in base 4, because
- 1 times m-reduction [i] would yield (151, 189, 2576347)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 615660 228672 855598 683934 788153 145662 521893 746622 453669 378217 681761 906411 387568 569949 593540 605698 048199 254908 185004 > 4189 [i]