Best Known (42, 56, s)-Nets in Base 128
(42, 56, 1198371)-Net over F128 — Constructive and digital
Digital (42, 56, 1198371)-net over F128, using
- 1 times m-reduction [i] based on digital (42, 57, 1198371)-net over F128, using
- net defined by OOA [i] based on linear OOA(12857, 1198371, F128, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12857, 8388598, F128, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12857, large, F128, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12857, large, F128, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12857, 8388598, F128, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(12857, 1198371, F128, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
(42, 56, 1198630)-Net in Base 128 — Constructive
(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
(42, 56, large)-Net over F128 — Digital
Digital (42, 56, large)-net over F128, using
- 1281 times duplication [i] based on digital (41, 55, large)-net over F128, using
- t-expansion [i] based on digital (40, 55, large)-net over F128, using
(42, 56, large)-Net in Base 128 — Upper bound on s
There is no (42, 56, large)-net in base 128, because
- 12 times m-reduction [i] would yield (42, 44, large)-net in base 128, but