Best Known (59, 78, s)-Nets in Base 128
(59, 78, 932067)-Net over F128 — Constructive and digital
Digital (59, 78, 932067)-net over F128, using
- 1282 times duplication [i] based on digital (57, 76, 932067)-net over F128, using
- net defined by OOA [i] based on linear OOA(12876, 932067, F128, 21, 19) (dual of [(932067, 21), 19573331, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(12876, 2796202, F128, 3, 19) (dual of [(2796202, 3), 8388530, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12873, 2796201, F128, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(12873, large, F128, 19) (dual of [large, large−73, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12873, 2796201, F128, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(12876, 2796202, F128, 3, 19) (dual of [(2796202, 3), 8388530, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12876, 932067, F128, 21, 19) (dual of [(932067, 21), 19573331, 20]-NRT-code), using
(59, 78, 932579)-Net in Base 128 — Constructive
(59, 78, 932579)-net in base 128, using
- (u, u+v)-construction [i] based on
- (6, 15, 513)-net in base 128, using
- net defined by OOA [i] based on OOA(12815, 513, S128, 12, 9), using
- OOA stacking with additional row [i] based on OOA(12815, 514, S128, 4, 9), using
- discarding parts of the base [i] based on linear OOA(25613, 514, F256, 4, 9) (dual of [(514, 4), 2043, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1024,256) [i]
- linear OOA(2569, 257, F256, 4, 9) (dual of [(257, 4), 1019, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1019,256) [i]
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding parts of the base [i] based on linear OOA(25613, 514, F256, 4, 9) (dual of [(514, 4), 2043, 10]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12815, 514, S128, 4, 9), using
- net defined by OOA [i] based on OOA(12815, 513, S128, 12, 9), 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
- (6, 15, 513)-net in base 128, using
(59, 78, large)-Net over F128 — Digital
Digital (59, 78, large)-net over F128, using
- 1281 times duplication [i] based on digital (58, 77, large)-net over F128, using
- t-expansion [i] based on digital (56, 77, large)-net over F128, using
(59, 78, large)-Net in Base 128 — Upper bound on s
There is no (59, 78, large)-net in base 128, because
- 17 times m-reduction [i] would yield (59, 61, large)-net in base 128, but