Best Known (85−15, 85, s)-Nets in Base 7
(85−15, 85, 117649)-Net over F7 — Constructive and digital
Digital (70, 85, 117649)-net over F7, using
- net defined by OOA [i] based on linear OOA(785, 117649, F7, 15, 15) (dual of [(117649, 15), 1764650, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(785, 823544, F7, 15) (dual of [823544, 823459, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 823544 | 714−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(785, 823544, F7, 15) (dual of [823544, 823459, 16]-code), using
(85−15, 85, 411772)-Net over F7 — Digital
Digital (70, 85, 411772)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(785, 411772, F7, 2, 15) (dual of [(411772, 2), 823459, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(785, 823544, F7, 15) (dual of [823544, 823459, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 823544 | 714−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 2-folding [i] based on linear OA(785, 823544, F7, 15) (dual of [823544, 823459, 16]-code), using
(85−15, 85, large)-Net in Base 7 — Upper bound on s
There is no (70, 85, large)-net in base 7, because
- 13 times m-reduction [i] would yield (70, 72, large)-net in base 7, but