Best Known (99−26, 99, s)-Nets in Base 32
(99−26, 99, 2628)-Net over F32 — Constructive and digital
Digital (73, 99, 2628)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 108)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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 (3, 16, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (1, 7, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (50, 76, 2520)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 2520, F32, 26, 26) (dual of [(2520, 26), 65444, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3276, 32760, F32, 26) (dual of [32760, 32684, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3276, 32760, F32, 26) (dual of [32760, 32684, 27]-code), using
- net defined by OOA [i] based on linear OOA(3276, 2520, F32, 26, 26) (dual of [(2520, 26), 65444, 27]-NRT-code), using
- digital (10, 23, 108)-net over F32, using
(99−26, 99, 20167)-Net in Base 32 — Constructive
(73, 99, 20167)-net in base 32, using
- net defined by OOA [i] based on OOA(3299, 20167, S32, 26, 26), using
- OA 13-folding and stacking [i] based on OA(3299, 262171, S32, 26), using
- discarding parts of the base [i] based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(646, 27, F64, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding parts of the base [i] based on linear OA(6482, 262171, F64, 26) (dual of [262171, 262089, 27]-code), using
- OA 13-folding and stacking [i] based on OA(3299, 262171, S32, 26), using
(99−26, 99, 299693)-Net over F32 — Digital
Digital (73, 99, 299693)-net over F32, using
(99−26, 99, large)-Net in Base 32 — Upper bound on s
There is no (73, 99, large)-net in base 32, because
- 24 times m-reduction [i] would yield (73, 75, large)-net in base 32, but