Best Known (38, 38+13, s)-Nets in Base 128
(38, 38+13, 1398100)-Net over F128 — Constructive and digital
Digital (38, 51, 1398100)-net over F128, using
- 1282 times duplication [i] based on digital (36, 49, 1398100)-net over F128, using
- net defined by OOA [i] based on linear OOA(12849, 1398100, F128, 13, 13) (dual of [(1398100, 13), 18175251, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12849, 8388601, F128, 13) (dual of [8388601, 8388552, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12849, large, F128, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12849, large, F128, 13) (dual of [large, large−49, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12849, 8388601, F128, 13) (dual of [8388601, 8388552, 14]-code), using
- net defined by OOA [i] based on linear OOA(12849, 1398100, F128, 13, 13) (dual of [(1398100, 13), 18175251, 14]-NRT-code), using
(38, 38+13, 1398358)-Net in Base 128 — Constructive
(38, 51, 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
- (30, 43, 1398100)-net in base 128, using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- discarding factors based on OA(12843, large, S128, 13), using
- discarding parts of the base [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding parts of the base [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- discarding factors based on OA(12843, large, S128, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
- (2, 8, 258)-net in base 128, using
(38, 38+13, large)-Net over F128 — Digital
Digital (38, 51, large)-net over F128, using
- 1 times m-reduction [i] based on digital (38, 52, large)-net over F128, using
(38, 38+13, large)-Net in Base 128 — Upper bound on s
There is no (38, 51, large)-net in base 128, because
- 11 times m-reduction [i] would yield (38, 40, large)-net in base 128, but