Best Known (109−15, 109, s)-Nets in Base 9
(109−15, 109, 1198371)-Net over F9 — Constructive and digital
Digital (94, 109, 1198371)-net over F9, using
- 94 times duplication [i] based on digital (90, 105, 1198371)-net over F9, using
- net defined by OOA [i] based on linear OOA(9105, 1198371, F9, 15, 15) (dual of [(1198371, 15), 17975460, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(9105, 8388598, F9, 15) (dual of [8388598, 8388493, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(9105, large, F9, 15) (dual of [large, large−105, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(9105, large, F9, 15) (dual of [large, large−105, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(9105, 8388598, F9, 15) (dual of [8388598, 8388493, 16]-code), using
- net defined by OOA [i] based on linear OOA(9105, 1198371, F9, 15, 15) (dual of [(1198371, 15), 17975460, 16]-NRT-code), using
(109−15, 109, large)-Net over F9 — Digital
Digital (94, 109, large)-net over F9, using
- 95 times duplication [i] based on digital (89, 104, large)-net over F9, using
(109−15, 109, large)-Net in Base 9 — Upper bound on s
There is no (94, 109, large)-net in base 9, because
- 13 times m-reduction [i] would yield (94, 96, large)-net in base 9, but