Best Known (14, 23, s)-Nets in Base 8
(14, 23, 160)-Net over F8 — Constructive and digital
Digital (14, 23, 160)-net over F8, using
- 3 times m-reduction [i] based on digital (14, 26, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 13, 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, 13, 80)-net over F64, using
(14, 23, 258)-Net in Base 8 — Constructive
(14, 23, 258)-net in base 8, using
- 1 times m-reduction [i] based on (14, 24, 258)-net in base 8, using
- trace code for nets [i] based on (2, 12, 129)-net in base 64, using
- 2 times m-reduction [i] based on (2, 14, 129)-net in base 64, using
- base change [i] based on digital (0, 12, 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, 12, 129)-net over F128, using
- 2 times m-reduction [i] based on (2, 14, 129)-net in base 64, using
- trace code for nets [i] based on (2, 12, 129)-net in base 64, using
(14, 23, 329)-Net over F8 — Digital
Digital (14, 23, 329)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(823, 329, F8, 9) (dual of [329, 306, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(823, 516, F8, 9) (dual of [516, 493, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(819, 512, F8, 7) (dual of [512, 493, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(823, 516, F8, 9) (dual of [516, 493, 10]-code), using
(14, 23, 29303)-Net in Base 8 — Upper bound on s
There is no (14, 23, 29304)-net in base 8, because
- 1 times m-reduction [i] would yield (14, 22, 29304)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 73 792348 150380 330703 > 822 [i]