Best Known (147−26, 147, s)-Nets in Base 4
(147−26, 147, 1268)-Net over F4 — Constructive and digital
Digital (121, 147, 1268)-net over F4, using
- 41 times duplication [i] based on digital (120, 146, 1268)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 42, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 14, 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, 14, 80)-net over F64, using
- digital (78, 104, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 26, 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, 26, 257)-net over F256, using
- digital (29, 42, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(147−26, 147, 15005)-Net over F4 — Digital
Digital (121, 147, 15005)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4147, 15005, F4, 26) (dual of [15005, 14858, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4147, 16398, F4, 26) (dual of [16398, 16251, 27]-code), using
- (u, u+v)-construction [i] based on
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- dual of repetition code with length 14 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4147, 16398, F4, 26) (dual of [16398, 16251, 27]-code), using
(147−26, 147, large)-Net in Base 4 — Upper bound on s
There is no (121, 147, large)-net in base 4, because
- 24 times m-reduction [i] would yield (121, 123, large)-net in base 4, but