Best Known (64, 64+14, s)-Nets in Base 128
(64, 64+14, 2396742)-Net over F128 — Constructive and digital
Digital (64, 78, 2396742)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (18, 25, 2796200)-net over F128, using
- net defined by OOA [i] based on linear OOA(12825, 2796200, F128, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(12825, 8388601, F128, 7) (dual of [8388601, 8388576, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(12825, large, F128, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(12825, large, F128, 7) (dual of [large, large−25, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(12825, 8388601, F128, 7) (dual of [8388601, 8388576, 8]-code), using
- net defined by OOA [i] based on linear OOA(12825, 2796200, F128, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- digital (39, 53, 1198371)-net over F128, using
- net defined by OOA [i] based on linear OOA(12853, 1198371, F128, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12853, 8388597, F128, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12853, large, F128, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(12853, large, F128, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12853, 8388597, F128, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(12853, 1198371, F128, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- digital (18, 25, 2796200)-net over F128, using
(64, 64+14, 2397260)-Net in Base 128 — Constructive
(64, 78, 2397260)-net in base 128, using
- (u, u+v)-construction [i] based on
- (15, 22, 2796200)-net in base 128, using
- net defined by OOA [i] based on OOA(12822, 2796200, S128, 7, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(12822, 8388601, S128, 7), using
- discarding factors based on OA(12822, large, S128, 7), using
- discarding parts of the base [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding parts of the base [i] based on linear OA(25619, large, F256, 7) (dual of [large, large−19, 8]-code), using
- discarding factors based on OA(12822, large, S128, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(12822, 8388601, S128, 7), using
- net defined by OOA [i] based on OOA(12822, 2796200, S128, 7, 7), using
- (42, 56, 1198630)-net in base 128, using
- base change [i] based on digital (35, 49, 1198630)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- digital (2, 9, 259)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (35, 49, 1198630)-net over F256, using
- (15, 22, 2796200)-net in base 128, using
(64, 64+14, large)-Net over F128 — Digital
Digital (64, 78, large)-net over F128, using
- 1281 times duplication [i] based on digital (63, 77, large)-net over F128, using
- t-expansion [i] based on digital (56, 77, large)-net over F128, using
(64, 64+14, large)-Net in Base 128 — Upper bound on s
There is no (64, 78, large)-net in base 128, because
- 12 times m-reduction [i] would yield (64, 66, large)-net in base 128, but