Best Known (125, 155, s)-Nets in Base 4
(125, 155, 1094)-Net over F4 — Constructive and digital
Digital (125, 155, 1094)-net over F4, using
- 41 times duplication [i] based on digital (124, 154, 1094)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (19, 34, 66)-net over F4, using
- trace code for nets [i] based on digital (2, 17, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- trace code for nets [i] based on digital (2, 17, 33)-net over F16, using
- digital (90, 120, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
- digital (19, 34, 66)-net over F4, using
- (u, u+v)-construction [i] based on
(125, 155, 8195)-Net over F4 — Digital
Digital (125, 155, 8195)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4155, 8195, F4, 2, 30) (dual of [(8195, 2), 16235, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4155, 16390, F4, 30) (dual of [16390, 16235, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4155, 16391, F4, 30) (dual of [16391, 16236, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 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(29) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4155, 16391, F4, 30) (dual of [16391, 16236, 31]-code), using
- OOA 2-folding [i] based on linear OA(4155, 16390, F4, 30) (dual of [16390, 16235, 31]-code), using
(125, 155, 3563940)-Net in Base 4 — Upper bound on s
There is no (125, 155, 3563941)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2085 925201 407495 849470 466589 722978 784588 838177 356056 942618 621630 721827 164350 400013 169350 860512 > 4155 [i]