Best Known (138, 167, s)-Nets in Base 4
(138, 167, 1340)-Net over F4 — Constructive and digital
Digital (138, 167, 1340)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (37, 51, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 17, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 17, 104)-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 (37, 51, 312)-net over F4, using
(138, 167, 1415)-Net in Base 4 — Constructive
(138, 167, 1415)-net in base 4, using
- (u, u+v)-construction [i] based on
- (37, 51, 387)-net in base 4, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 18, 129)-net over F128, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, 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
- (37, 51, 387)-net in base 4, using
(138, 167, 16450)-Net over F4 — Digital
Digital (138, 167, 16450)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4167, 16450, F4, 29) (dual of [16450, 16283, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(18) [i] based on
- 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(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(419, 66, F4, 9) (dual of [66, 47, 10]-code), using
- construction X applied to Ce(28) ⊂ Ce(18) [i] based on
(138, 167, large)-Net in Base 4 — Upper bound on s
There is no (138, 167, large)-net in base 4, because
- 27 times m-reduction [i] would yield (138, 140, large)-net in base 4, but