Best Known (33, 33+13, s)-Nets in Base 32
(33, 33+13, 5527)-Net over F32 — Constructive and digital
Digital (33, 46, 5527)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 66)-net over F32, using
- (u, u+v)-construction [i] based on
- 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, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (24, 37, 5461)-net over F32, using
- net defined by OOA [i] based on linear OOA(3237, 5461, F32, 13, 13) (dual of [(5461, 13), 70956, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
- net defined by OOA [i] based on linear OOA(3237, 5461, F32, 13, 13) (dual of [(5461, 13), 70956, 14]-NRT-code), using
- digital (3, 9, 66)-net over F32, using
(33, 33+13, 43691)-Net in Base 32 — Constructive
(33, 46, 43691)-net in base 32, using
- 321 times duplication [i] based on (32, 45, 43691)-net in base 32, using
- net defined by OOA [i] based on OOA(3245, 43691, S32, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3245, 262147, S32, 13), using
- discarding parts of the base [i] based on linear OA(6437, 262147, F64, 13) (dual of [262147, 262110, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(6437, 262147, F64, 13) (dual of [262147, 262110, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on OA(3245, 262147, S32, 13), using
- net defined by OOA [i] based on OOA(3245, 43691, S32, 13, 13), using
(33, 33+13, 100408)-Net over F32 — Digital
Digital (33, 46, 100408)-net over F32, using
(33, 33+13, large)-Net in Base 32 — Upper bound on s
There is no (33, 46, large)-net in base 32, because
- 11 times m-reduction [i] would yield (33, 35, large)-net in base 32, but