Best Known (87, 87+14, s)-Nets in Base 9
(87, 87+14, 1198371)-Net over F9 — Constructive and digital
Digital (87, 101, 1198371)-net over F9, using
- 94 times duplication [i] based on digital (83, 97, 1198371)-net over F9, using
- net defined by OOA [i] based on linear OOA(997, 1198371, F9, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(997, 8388597, F9, 14) (dual of [8388597, 8388500, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(997, large, F9, 14) (dual of [large, large−97, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(997, large, F9, 14) (dual of [large, large−97, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(997, 8388597, F9, 14) (dual of [8388597, 8388500, 15]-code), using
- net defined by OOA [i] based on linear OOA(997, 1198371, F9, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
(87, 87+14, large)-Net over F9 — Digital
Digital (87, 101, large)-net over F9, using
- 94 times duplication [i] based on digital (83, 97, large)-net over F9, using
(87, 87+14, large)-Net in Base 9 — Upper bound on s
There is no (87, 101, large)-net in base 9, because
- 12 times m-reduction [i] would yield (87, 89, large)-net in base 9, but