Best Known (73, 98, s)-Nets in Base 9
(73, 98, 1093)-Net over F9 — Constructive and digital
Digital (73, 98, 1093)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 1093, F9, 25, 25) (dual of [(1093, 25), 27227, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(998, 13117, F9, 25) (dual of [13117, 13019, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(998, 13117, F9, 25) (dual of [13117, 13019, 26]-code), using
(73, 98, 12454)-Net over F9 — Digital
Digital (73, 98, 12454)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(998, 12454, F9, 25) (dual of [12454, 12356, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
(73, 98, large)-Net in Base 9 — Upper bound on s
There is no (73, 98, large)-net in base 9, because
- 23 times m-reduction [i] would yield (73, 75, large)-net in base 9, but