Best Known (21, 34, s)-Nets in Base 32
(21, 34, 330)-Net over F32 — Constructive and digital
Digital (21, 34, 330)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 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 (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 13, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(21, 34, 684)-Net in Base 32 — Constructive
(21, 34, 684)-net in base 32, using
- net defined by OOA [i] based on OOA(3234, 684, S32, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3234, 4105, S32, 13), using
- discarding factors based on OA(3234, 4108, S32, 13), using
- discarding parts of the base [i] based on linear OA(6428, 4108, F64, 13) (dual of [4108, 4080, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- discarding parts of the base [i] based on linear OA(6428, 4108, F64, 13) (dual of [4108, 4080, 14]-code), using
- discarding factors based on OA(3234, 4108, S32, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3234, 4105, S32, 13), using
(21, 34, 3144)-Net over F32 — Digital
Digital (21, 34, 3144)-net over F32, using
(21, 34, large)-Net in Base 32 — Upper bound on s
There is no (21, 34, large)-net in base 32, because
- 11 times m-reduction [i] would yield (21, 23, large)-net in base 32, but