Best Known (183−34, 183, s)-Nets in Base 4
(183−34, 183, 1158)-Net over F4 — Constructive and digital
Digital (149, 183, 1158)-net over F4, using
- 41 times duplication [i] based on digital (148, 182, 1158)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 46, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 23, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 23, 65)-net over F16, using
- digital (102, 136, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 34, 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, 34, 257)-net over F256, using
- digital (29, 46, 130)-net over F4, using
- (u, u+v)-construction [i] based on
(183−34, 183, 11298)-Net over F4 — Digital
Digital (149, 183, 11298)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 11298, F4, 34) (dual of [11298, 11115, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 16419, F4, 34) (dual of [16419, 16236, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4183, 16419, F4, 34) (dual of [16419, 16236, 35]-code), using
(183−34, 183, 7241388)-Net in Base 4 — Upper bound on s
There is no (149, 183, 7241389)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 150 306815 742321 849221 535674 969403 048601 915290 214832 691983 301880 749296 057735 116091 603334 062372 625728 480141 759920 > 4183 [i]