Best Known (30, 30+25, s)-Nets in Base 32
(30, 30+25, 218)-Net over F32 — Constructive and digital
Digital (30, 55, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (11, 36, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (7, 19, 98)-net over F32, using
(30, 30+25, 322)-Net in Base 32 — Constructive
(30, 55, 322)-net in base 32, using
- (u, u+v)-construction [i] based on
- (3, 15, 65)-net in base 32, using
- 3 times m-reduction [i] based on (3, 18, 65)-net in base 32, using
- base change [i] based on digital (0, 15, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 15, 65)-net over F64, using
- 3 times m-reduction [i] based on (3, 18, 65)-net in base 32, using
- (15, 40, 257)-net in base 32, using
- base change [i] based on digital (0, 25, 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, 25, 257)-net over F256, using
- (3, 15, 65)-net in base 32, using
(30, 30+25, 1029)-Net over F32 — Digital
Digital (30, 55, 1029)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3255, 1029, F32, 25) (dual of [1029, 974, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3255, 1044, F32, 25) (dual of [1044, 989, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(3249, 1024, F32, 25) (dual of [1024, 975, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3235, 1024, F32, 18) (dual of [1024, 989, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(326, 20, F32, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(3255, 1044, F32, 25) (dual of [1044, 989, 26]-code), using
(30, 30+25, 1011980)-Net in Base 32 — Upper bound on s
There is no (30, 55, 1011981)-net in base 32, because
- 1 times m-reduction [i] would yield (30, 54, 1011981)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1897 151368 749853 615009 938667 464252 769884 830900 698961 186230 725469 657211 340964 027937 > 3254 [i]