Best Known (63−29, 63, s)-Nets in Base 32
(63−29, 63, 224)-Net over F32 — Constructive and digital
Digital (34, 63, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (11, 40, 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 (9, 23, 104)-net over F32, using
(63−29, 63, 302)-Net in Base 32 — Constructive
(34, 63, 302)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- (19, 48, 258)-net in base 32, using
- base change [i] based on digital (1, 30, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 30, 258)-net over F256, using
- digital (1, 15, 44)-net over F32, using
(63−29, 63, 995)-Net over F32 — Digital
Digital (34, 63, 995)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3263, 995, F32, 29) (dual of [995, 932, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3263, 1044, F32, 29) (dual of [1044, 981, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(3257, 1024, F32, 29) (dual of [1024, 967, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3243, 1024, F32, 22) (dual of [1024, 981, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(28) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3263, 1044, F32, 29) (dual of [1044, 981, 30]-code), using
(63−29, 63, 903143)-Net in Base 32 — Upper bound on s
There is no (34, 63, 903144)-net in base 32, because
- 1 times m-reduction [i] would yield (34, 62, 903144)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2085 932139 179119 285951 126839 477409 995993 191116 375540 237845 704685 439410 262855 664966 524899 942068 > 3262 [i]