Best Known (18, 18+7, s)-Nets in Base 128
(18, 18+7, 2796200)-Net over F128 — Constructive and digital
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
(18, 18+7, 2796329)-Net in Base 128 — Constructive
(18, 25, 2796329)-net in base 128, using
- net defined by OOA [i] based on OOA(12825, 2796329, S128, 9, 7), using
- OOA stacking with additional row [i] based on OOA(12825, 2796330, S128, 3, 7), using
- (u, u+v)-construction [i] based on
- linear OOA(1283, 129, F128, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;384,128) [i]
- OOA(12822, 2796201, S128, 3, 7), using
- OOA 3-folding [i] 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
- OOA 3-folding [i] based on OA(12822, large, S128, 7), using
- linear OOA(1283, 129, F128, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(12825, 2796330, S128, 3, 7), using
(18, 18+7, large)-Net over F128 — Digital
Digital (18, 25, large)-net over F128, using
(18, 18+7, large)-Net in Base 128 — Upper bound on s
There is no (18, 25, large)-net in base 128, because
- 5 times m-reduction [i] would yield (18, 20, large)-net in base 128, but