Best Known (58, 58+18, s)-Nets in Base 9
(58, 58+18, 1460)-Net over F9 — Constructive and digital
Digital (58, 76, 1460)-net over F9, using
- net defined by OOA [i] based on linear OOA(976, 1460, F9, 18, 18) (dual of [(1460, 18), 26204, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(976, 13140, F9, 18) (dual of [13140, 13064, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(976, 13144, F9, 18) (dual of [13144, 13068, 19]-code), using
- trace code [i] based on linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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 Ce(17) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(976, 13144, F9, 18) (dual of [13144, 13068, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(976, 13140, F9, 18) (dual of [13140, 13064, 19]-code), using
(58, 58+18, 16562)-Net over F9 — Digital
Digital (58, 76, 16562)-net over F9, using
(58, 58+18, large)-Net in Base 9 — Upper bound on s
There is no (58, 76, large)-net in base 9, because
- 16 times m-reduction [i] would yield (58, 60, large)-net in base 9, but