Best Known (62, 96, s)-Nets in Base 32
(62, 96, 371)-Net over F32 — Constructive and digital
Digital (62, 96, 371)-net over F32, using
- 1 times m-reduction [i] based on digital (62, 97, 371)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- 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
- (u, u+v)-construction [i] based on
- digital (7, 18, 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 (7, 24, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 42, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (5, 13, 77)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(62, 96, 964)-Net in Base 32 — Constructive
(62, 96, 964)-net in base 32, using
- net defined by OOA [i] based on OOA(3296, 964, S32, 34, 34), using
- OA 17-folding and stacking [i] based on OA(3296, 16388, S32, 34), using
- discarding factors based on OA(3296, 16389, S32, 34), using
- discarding parts of the base [i] based on linear OA(12868, 16389, F128, 34) (dual of [16389, 16321, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(31) [i] based on
- linear OA(12867, 16384, F128, 34) (dual of [16384, 16317, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(12863, 16384, F128, 32) (dual of [16384, 16321, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(31) [i] based on
- discarding parts of the base [i] based on linear OA(12868, 16389, F128, 34) (dual of [16389, 16321, 35]-code), using
- discarding factors based on OA(3296, 16389, S32, 34), using
- OA 17-folding and stacking [i] based on OA(3296, 16388, S32, 34), using
(62, 96, 10170)-Net over F32 — Digital
Digital (62, 96, 10170)-net over F32, using
(62, 96, large)-Net in Base 32 — Upper bound on s
There is no (62, 96, large)-net in base 32, because
- 32 times m-reduction [i] would yield (62, 64, large)-net in base 32, but