Best Known (140, 140+30, s)-Nets in Base 4
(140, 140+30, 1268)-Net over F4 — Constructive and digital
Digital (140, 170, 1268)-net over F4, using
- 42 times duplication [i] based on digital (138, 168, 1268)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 48, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 16, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 16, 80)-net over F64, 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 (33, 48, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(140, 140+30, 16186)-Net over F4 — Digital
Digital (140, 170, 16186)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4170, 16186, F4, 30) (dual of [16186, 16016, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4170, 16400, F4, 30) (dual of [16400, 16230, 31]-code), using
- (u, u+v)-construction [i] based on
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- 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(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4170, 16400, F4, 30) (dual of [16400, 16230, 31]-code), using
(140, 140+30, large)-Net in Base 4 — Upper bound on s
There is no (140, 170, large)-net in base 4, because
- 28 times m-reduction [i] would yield (140, 142, large)-net in base 4, but