Best Known (70, 70+15, s)-Nets in Base 16
(70, 70+15, 1198371)-Net over F16 — Constructive and digital
Digital (70, 85, 1198371)-net over F16, using
- net defined by OOA [i] based on linear OOA(1685, 1198371, F16, 15, 15) (dual of [(1198371, 15), 17975480, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(1685, 8388598, F16, 15) (dual of [8388598, 8388513, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(1685, large, F16, 15) (dual of [large, large−85, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(1685, large, F16, 15) (dual of [large, large−85, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(1685, 8388598, F16, 15) (dual of [8388598, 8388513, 16]-code), using
(70, 70+15, large)-Net over F16 — Digital
Digital (70, 85, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1685, large, F16, 15) (dual of [large, large−85, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
(70, 70+15, large)-Net in Base 16 — Upper bound on s
There is no (70, 85, large)-net in base 16, because
- 13 times m-reduction [i] would yield (70, 72, large)-net in base 16, but