Best Known (38−14, 38, s)-Nets in Base 8
(38−14, 38, 256)-Net over F8 — Constructive and digital
Digital (24, 38, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 19, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(38−14, 38, 454)-Net over F8 — Digital
Digital (24, 38, 454)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(838, 454, F8, 14) (dual of [454, 416, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 519, F8, 14) (dual of [519, 481, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(837, 512, F8, 14) (dual of [512, 475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(831, 512, F8, 12) (dual of [512, 481, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 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(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(838, 519, F8, 14) (dual of [519, 481, 15]-code), using
(38−14, 38, 514)-Net in Base 8 — Constructive
(24, 38, 514)-net in base 8, using
- trace code for nets [i] based on (5, 19, 257)-net in base 64, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
- base change [i] based on digital (0, 15, 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
- base change [i] based on digital (0, 15, 257)-net over F256, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
(38−14, 38, 38571)-Net in Base 8 — Upper bound on s
There is no (24, 38, 38572)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 20771 893334 973214 535592 563450 523566 > 838 [i]