Best Known (77, 96, s)-Nets in Base 32
(77, 96, 932066)-Net over F32 — Constructive and digital
Digital (77, 96, 932066)-net over F32, using
- 325 times duplication [i] based on digital (72, 91, 932066)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
(77, 96, 932067)-Net in Base 32 — Constructive
(77, 96, 932067)-net in base 32, using
- base change [i] based on digital (61, 80, 932067)-net over F64, using
- 644 times duplication [i] based on digital (57, 76, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6476, 932067, F64, 21, 19) (dual of [(932067, 21), 19573331, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(6476, 2796202, F64, 3, 19) (dual of [(2796202, 3), 8388530, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(6476, 2796202, F64, 3, 19) (dual of [(2796202, 3), 8388530, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6476, 932067, F64, 21, 19) (dual of [(932067, 21), 19573331, 20]-NRT-code), using
- 644 times duplication [i] based on digital (57, 76, 932067)-net over F64, using
(77, 96, large)-Net over F32 — Digital
Digital (77, 96, large)-net over F32, using
- 321 times duplication [i] based on digital (76, 95, large)-net over F32, using
- t-expansion [i] based on digital (75, 95, large)-net over F32, using
(77, 96, large)-Net in Base 32 — Upper bound on s
There is no (77, 96, large)-net in base 32, because
- 17 times m-reduction [i] would yield (77, 79, large)-net in base 32, but