Best Known (32−6, 32, s)-Nets in Base 32
(32−6, 32, 2831051)-Net over F32 — Constructive and digital
Digital (26, 32, 2831051)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 6, 34850)-net over F32, using
- net defined by OOA [i] based on linear OOA(326, 34850, F32, 3, 3) (dual of [(34850, 3), 104544, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(326, 34850, F32, 2, 3) (dual of [(34850, 2), 69694, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(326, 34850, F32, 3, 3) (dual of [(34850, 3), 104544, 4]-NRT-code), using
- digital (20, 26, 2796201)-net over F32, using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- digital (3, 6, 34850)-net over F32, using
(32−6, 32, 2861738)-Net in Base 32 — Constructive
(26, 32, 2861738)-net in base 32, using
- base change [i] based on digital (14, 20, 2861738)-net over F256, using
- net defined by OOA [i] based on linear OOA(25620, 2861738, F256, 6, 6) (dual of [(2861738, 6), 17170408, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(25620, 2861738, F256, 5, 6) (dual of [(2861738, 5), 14308670, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 65537, F256, 5, 3) (dual of [(65537, 5), 327681, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2564, 65537, F256, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(2564, 65537, F256, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2564, 65537, F256, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
- linear OOA(25616, 2796201, F256, 5, 6) (dual of [(2796201, 5), 13980989, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- linear OOA(2564, 65537, F256, 5, 3) (dual of [(65537, 5), 327681, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(25620, 2861738, F256, 5, 6) (dual of [(2861738, 5), 14308670, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25620, 2861738, F256, 6, 6) (dual of [(2861738, 6), 17170408, 7]-NRT-code), using
(32−6, 32, large)-Net over F32 — Digital
Digital (26, 32, large)-net over F32, using
- 321 times duplication [i] based on digital (25, 31, large)-net over F32, using
- t-expansion [i] based on digital (24, 31, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- t-expansion [i] based on digital (24, 31, large)-net over F32, using
(32−6, 32, large)-Net in Base 32 — Upper bound on s
There is no (26, 32, large)-net in base 32, because
- 4 times m-reduction [i] would yield (26, 28, large)-net in base 32, but