Best Known (56, 75, s)-Nets in Base 128
(56, 75, 932066)-Net over F128 — Constructive and digital
Digital (56, 75, 932066)-net over F128, using
- 1282 times duplication [i] based on digital (54, 73, 932066)-net over F128, using
- net defined by OOA [i] based on linear OOA(12873, 932066, F128, 19, 19) (dual of [(932066, 19), 17709181, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12873, 8388595, F128, 19) (dual of [8388595, 8388522, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, large, F128, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, 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(12873, large, F128, 19) (dual of [large, large−73, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12873, 8388595, F128, 19) (dual of [8388595, 8388522, 20]-code), using
- net defined by OOA [i] based on linear OOA(12873, 932066, F128, 19, 19) (dual of [(932066, 19), 17709181, 20]-NRT-code), using
(56, 75, 932324)-Net in Base 128 — Constructive
(56, 75, 932324)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 12, 258)-net in base 128, using
- 4 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- 4 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- (44, 63, 932066)-net in base 128, using
- net defined by OOA [i] based on OOA(12863, 932066, S128, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(12863, 8388595, S128, 19), using
- discarding factors based on OA(12863, large, S128, 19), using
- discarding parts of the base [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding parts of the base [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- discarding factors based on OA(12863, large, S128, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(12863, 8388595, S128, 19), using
- net defined by OOA [i] based on OOA(12863, 932066, S128, 19, 19), using
- (3, 12, 258)-net in base 128, using
(56, 75, large)-Net over F128 — Digital
Digital (56, 75, large)-net over F128, using
- 2 times m-reduction [i] based on digital (56, 77, large)-net over F128, using
(56, 75, large)-Net in Base 128 — Upper bound on s
There is no (56, 75, large)-net in base 128, because
- 17 times m-reduction [i] would yield (56, 58, large)-net in base 128, but