Best Known (73−13, 73, s)-Nets in Base 16
(73−13, 73, 1398100)-Net over F16 — Constructive and digital
Digital (60, 73, 1398100)-net over F16, using
- net defined by OOA [i] based on linear OOA(1673, 1398100, F16, 13, 13) (dual of [(1398100, 13), 18175227, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(1673, 8388601, F16, 13) (dual of [8388601, 8388528, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(1673, 8388601, F16, 13) (dual of [8388601, 8388528, 14]-code), using
(73−13, 73, large)-Net over F16 — Digital
Digital (60, 73, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
(73−13, 73, large)-Net in Base 16 — Upper bound on s
There is no (60, 73, large)-net in base 16, because
- 11 times m-reduction [i] would yield (60, 62, large)-net in base 16, but