Best Known (26−7, 26, s)-Nets in Base 128
(26−7, 26, 2796200)-Net over F128 — Constructive and digital
Digital (19, 26, 2796200)-net over F128, using
- 1281 times duplication [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
(26−7, 26, 2812585)-Net in Base 128 — Constructive
(19, 26, 2812585)-net in base 128, using
- net defined by OOA [i] based on OOA(12826, 2812585, S128, 9, 7), using
- OOA stacking with additional row [i] based on OOA(12826, 2812586, S128, 3, 7), using
- (u, u+v)-construction [i] based on
- linear OOA(1284, 16385, F128, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1284, 16385, F128, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
- 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(1284, 16385, F128, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(12826, 2812586, S128, 3, 7), using
(26−7, 26, large)-Net over F128 — Digital
Digital (19, 26, large)-net over F128, using
- 1281 times duplication [i] based on digital (18, 25, large)-net over F128, using
(26−7, 26, large)-Net in Base 128 — Upper bound on s
There is no (19, 26, large)-net in base 128, because
- 5 times m-reduction [i] would yield (19, 21, large)-net in base 128, but