Best Known (74, 97, s)-Nets in Base 9
(74, 97, 1195)-Net over F9 — Constructive and digital
Digital (74, 97, 1195)-net over F9, using
- 91 times duplication [i] based on digital (73, 96, 1195)-net over F9, using
- net defined by OOA [i] based on linear OOA(996, 1195, F9, 23, 23) (dual of [(1195, 23), 27389, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(996, 13146, F9, 23) (dual of [13146, 13050, 24]-code), using
- trace code [i] based on linear OA(8148, 6573, F81, 23) (dual of [6573, 6525, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(8145, 6562, F81, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- trace code [i] based on linear OA(8148, 6573, F81, 23) (dual of [6573, 6525, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(996, 13146, F9, 23) (dual of [13146, 13050, 24]-code), using
- net defined by OOA [i] based on linear OOA(996, 1195, F9, 23, 23) (dual of [(1195, 23), 27389, 24]-NRT-code), using
(74, 97, 18254)-Net over F9 — Digital
Digital (74, 97, 18254)-net over F9, using
(74, 97, large)-Net in Base 9 — Upper bound on s
There is no (74, 97, large)-net in base 9, because
- 21 times m-reduction [i] would yield (74, 76, large)-net in base 9, but