Best Known (86, 86+14, s)-Nets in Base 32
(86, 86+14, 2396742)-Net over F32 — Constructive and digital
Digital (86, 100, 2396742)-net over F32, using
- 323 times duplication [i] based on digital (83, 97, 2396742)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (24, 31, 2796200)-net over F32, using
- net defined by OOA [i] based on linear OOA(3231, 2796200, F32, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3231, 8388601, F32, 7) (dual of [8388601, 8388570, 8]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3231, 8388601, F32, 7) (dual of [8388601, 8388570, 8]-code), using
- net defined by OOA [i] based on linear OOA(3231, 2796200, F32, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- digital (52, 66, 1198371)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (24, 31, 2796200)-net over F32, using
- (u, u+v)-construction [i] based on
(86, 86+14, large)-Net over F32 — Digital
Digital (86, 100, large)-net over F32, using
- t-expansion [i] based on digital (83, 100, large)-net over F32, using
- 5 times m-reduction [i] based on digital (83, 105, large)-net over F32, using
(86, 86+14, large)-Net in Base 32 — Upper bound on s
There is no (86, 100, large)-net in base 32, because
- 12 times m-reduction [i] would yield (86, 88, large)-net in base 32, but