Best Known (38, 38+14, s)-Nets in Base 32
(38, 38+14, 4780)-Net over F32 — Constructive and digital
Digital (38, 52, 4780)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 12, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- 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, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (26, 40, 4681)-net over F32, using
- net defined by OOA [i] based on linear OOA(3240, 4681, F32, 14, 14) (dual of [(4681, 14), 65494, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
- net defined by OOA [i] based on linear OOA(3240, 4681, F32, 14, 14) (dual of [(4681, 14), 65494, 15]-NRT-code), using
- digital (5, 12, 99)-net over F32, using
(38, 38+14, 37451)-Net in Base 32 — Constructive
(38, 52, 37451)-net in base 32, using
- net defined by OOA [i] based on OOA(3252, 37451, S32, 14, 14), using
- OA 7-folding and stacking [i] based on OA(3252, 262157, S32, 14), using
- discarding factors based on OA(3252, 262159, S32, 14), using
- discarding parts of the base [i] based on linear OA(6443, 262159, F64, 14) (dual of [262159, 262116, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(643, 15, F64, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-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 Ce(13) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(6443, 262159, F64, 14) (dual of [262159, 262116, 15]-code), using
- discarding factors based on OA(3252, 262159, S32, 14), using
- OA 7-folding and stacking [i] based on OA(3252, 262157, S32, 14), using
(38, 38+14, 191716)-Net over F32 — Digital
Digital (38, 52, 191716)-net over F32, using
(38, 38+14, large)-Net in Base 32 — Upper bound on s
There is no (38, 52, large)-net in base 32, because
- 12 times m-reduction [i] would yield (38, 40, large)-net in base 32, but