Best Known (162−29, 162, s)-Nets in Base 4
(162−29, 162, 1268)-Net over F4 — Constructive and digital
Digital (133, 162, 1268)-net over F4, using
- 41 times duplication [i] based on digital (132, 161, 1268)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (31, 45, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 15, 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, 15, 80)-net over F64, using
- digital (87, 116, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 29, 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, 29, 257)-net over F256, using
- digital (31, 45, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(162−29, 162, 14148)-Net over F4 — Digital
Digital (133, 162, 14148)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4162, 14148, F4, 29) (dual of [14148, 13986, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 16399, F4, 29) (dual of [16399, 16237, 30]-code), using
- (u, u+v)-construction [i] based on
- linear OA(414, 15, F4, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,4)), using
- dual of repetition code with length 15 [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(414, 15, F4, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4162, 16399, F4, 29) (dual of [16399, 16237, 30]-code), using
(162−29, 162, large)-Net in Base 4 — Upper bound on s
There is no (133, 162, large)-net in base 4, because
- 27 times m-reduction [i] would yield (133, 135, large)-net in base 4, but