Best Known (189−36, 189, s)-Nets in Base 4
(189−36, 189, 1118)-Net over F4 — Constructive and digital
Digital (153, 189, 1118)-net over F4, using
- 41 times duplication [i] based on digital (152, 188, 1118)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (26, 44, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 22, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- trace code for nets [i] based on digital (4, 22, 45)-net over F16, using
- digital (108, 144, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 36, 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, 36, 257)-net over F256, using
- digital (26, 44, 90)-net over F4, using
- (u, u+v)-construction [i] based on
(189−36, 189, 9598)-Net over F4 — Digital
Digital (153, 189, 9598)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4189, 9598, F4, 36) (dual of [9598, 9409, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4189, 16383, F4, 36) (dual of [16383, 16194, 37]-code), using
- 1 times truncation [i] based on linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4189, 16383, F4, 36) (dual of [16383, 16194, 37]-code), using
(189−36, 189, 5280043)-Net in Base 4 — Upper bound on s
There is no (153, 189, 5280044)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 615656 943561 339093 433853 184924 742567 549194 485549 311960 704077 460006 989322 022301 628350 936190 052198 441570 759336 855774 > 4189 [i]