Best Known (110, 110+19, s)-Nets in Base 8
(110, 110+19, 932066)-Net over F8 — Constructive and digital
Digital (110, 129, 932066)-net over F8, using
- net defined by OOA [i] based on linear OOA(8129, 932066, F8, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
(110, 110+19, 6465214)-Net over F8 — Digital
Digital (110, 129, 6465214)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8129, 6465214, F8, 19) (dual of [6465214, 6465085, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
(110, 110+19, large)-Net in Base 8 — Upper bound on s
There is no (110, 129, large)-net in base 8, because
- 17 times m-reduction [i] would yield (110, 112, large)-net in base 8, but