Best Known (35, 35+12, s)-Nets in Base 128
(35, 35+12, 1398100)-Net over F128 — Constructive and digital
Digital (35, 47, 1398100)-net over F128, using
- 1282 times duplication [i] based on digital (33, 45, 1398100)-net over F128, using
- net defined by OOA [i] based on linear OOA(12845, 1398100, F128, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12845, 8388600, F128, 12) (dual of [8388600, 8388555, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12845, 8388600, F128, 12) (dual of [8388600, 8388555, 13]-code), using
- net defined by OOA [i] based on linear OOA(12845, 1398100, F128, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
(35, 35+12, 1398358)-Net in Base 128 — Constructive
(35, 47, 1398358)-net in base 128, using
- (u, u+v)-construction [i] based on
- (2, 8, 258)-net in base 128, using
- base change [i] based on digital (1, 7, 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, 7, 258)-net over F256, using
- (27, 39, 1398100)-net in base 128, using
- net defined by OOA [i] based on OOA(12839, 1398100, S128, 12, 12), using
- OA 6-folding and stacking [i] based on OA(12839, 8388600, S128, 12), using
- discarding factors based on OA(12839, large, S128, 12), using
- discarding parts of the base [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding parts of the base [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- discarding factors based on OA(12839, large, S128, 12), using
- OA 6-folding and stacking [i] based on OA(12839, 8388600, S128, 12), using
- net defined by OOA [i] based on OOA(12839, 1398100, S128, 12, 12), using
- (2, 8, 258)-net in base 128, using
(35, 35+12, large)-Net over F128 — Digital
Digital (35, 47, large)-net over F128, using
- 1 times m-reduction [i] based on digital (35, 48, large)-net over F128, using
(35, 35+12, large)-Net in Base 128 — Upper bound on s
There is no (35, 47, large)-net in base 128, because
- 10 times m-reduction [i] would yield (35, 37, large)-net in base 128, but