Best Known (13−8, 13, s)-Nets in Base 32
(13−8, 13, 77)-Net over F32 — Constructive and digital
Digital (5, 13, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (1, 9, 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
- digital (0, 4, 33)-net over F32, using
(13−8, 13, 96)-Net over F32 — Digital
Digital (5, 13, 96)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3213, 96, F32, 8) (dual of [96, 83, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3213, 94, F32, 8) (dual of [94, 81, 9]-code), using an extension Ce(7) of the narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3211, 94, F32, 7) (dual of [94, 83, 8]-code), using an extension Ce(6) of the narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
(13−8, 13, 150)-Net in Base 32 — Constructive
(5, 13, 150)-net in base 32, using
- 1 times m-reduction [i] based on (5, 14, 150)-net in base 32, using
- base change [i] based on digital (1, 10, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 10, 150)-net over F128, using
(13−8, 13, 5562)-Net in Base 32 — Upper bound on s
There is no (5, 13, 5563)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 36 896090 968760 844334 > 3213 [i]