Best Known (183−35, 183, s)-Nets in Base 4
(183−35, 183, 1118)-Net over F4 — Constructive and digital
Digital (148, 183, 1118)-net over F4, using
- 41 times duplication [i] based on digital (147, 182, 1118)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (25, 42, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 21, 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, 21, 45)-net over F16, using
- digital (105, 140, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 35, 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, 35, 257)-net over F256, using
- digital (25, 42, 90)-net over F4, using
- (u, u+v)-construction [i] based on
(183−35, 183, 9150)-Net over F4 — Digital
Digital (148, 183, 9150)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 9150, F4, 35) (dual of [9150, 8967, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using
(183−35, 183, 6674311)-Net in Base 4 — Upper bound on s
There is no (148, 183, 6674312)-net in base 4, because
- 1 times m-reduction [i] would yield (148, 182, 6674312)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 37 576688 901051 144864 052910 943864 115359 026387 686391 692229 858415 473309 876281 914929 711523 271864 004067 491079 128680 > 4182 [i]