Best Known (109−15, 109, s)-Nets in Base 8
(109−15, 109, 1198371)-Net over F8 — Constructive and digital
Digital (94, 109, 1198371)-net over F8, using
- 84 times duplication [i] based on digital (90, 105, 1198371)-net over F8, using
- net defined by OOA [i] based on linear OOA(8105, 1198371, F8, 15, 15) (dual of [(1198371, 15), 17975460, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8105, 8388598, F8, 15) (dual of [8388598, 8388493, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8105, 8388598, F8, 15) (dual of [8388598, 8388493, 16]-code), using
- net defined by OOA [i] based on linear OOA(8105, 1198371, F8, 15, 15) (dual of [(1198371, 15), 17975460, 16]-NRT-code), using
(109−15, 109, large)-Net over F8 — Digital
Digital (94, 109, large)-net over F8, using
- 84 times duplication [i] based on digital (90, 105, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
(109−15, 109, large)-Net in Base 8 — Upper bound on s
There is no (94, 109, large)-net in base 8, because
- 13 times m-reduction [i] would yield (94, 96, large)-net in base 8, but