Best Known (32, 50, s)-Nets in Base 8
(32, 50, 354)-Net over F8 — Constructive and digital
Digital (32, 50, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(32, 50, 514)-Net in Base 8 — Constructive
(32, 50, 514)-net in base 8, using
- 82 times duplication [i] based on (30, 48, 514)-net in base 8, using
- base change [i] based on digital (18, 36, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 18, 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, 18, 257)-net over F256, using
- base change [i] based on digital (18, 36, 514)-net over F16, using
(32, 50, 535)-Net over F8 — Digital
Digital (32, 50, 535)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(850, 535, F8, 18) (dual of [535, 485, 19]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 0, 1, 10 times 0) [i] based on linear OA(846, 515, F8, 18) (dual of [515, 469, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(846, 512, F8, 18) (dual of [512, 466, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(843, 512, F8, 17) (dual of [512, 469, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- 16 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 0, 1, 10 times 0) [i] based on linear OA(846, 515, F8, 18) (dual of [515, 469, 19]-code), using
(32, 50, 61628)-Net in Base 8 — Upper bound on s
There is no (32, 50, 61629)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1427 317607 012088 615975 243012 956124 912538 866564 > 850 [i]