Best Known (68, 90, s)-Nets in Base 9
(68, 90, 1194)-Net over F9 — Constructive and digital
Digital (68, 90, 1194)-net over F9, using
- net defined by OOA [i] based on linear OOA(990, 1194, F9, 22, 22) (dual of [(1194, 22), 26178, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(990, 13134, F9, 22) (dual of [13134, 13044, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(990, 13138, F9, 22) (dual of [13138, 13048, 23]-code), using
- trace code [i] based on linear OA(8145, 6569, F81, 22) (dual of [6569, 6524, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- trace code [i] based on linear OA(8145, 6569, F81, 22) (dual of [6569, 6524, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(990, 13138, F9, 22) (dual of [13138, 13048, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(990, 13134, F9, 22) (dual of [13134, 13044, 23]-code), using
(68, 90, 13346)-Net over F9 — Digital
Digital (68, 90, 13346)-net over F9, using
(68, 90, large)-Net in Base 9 — Upper bound on s
There is no (68, 90, large)-net in base 9, because
- 20 times m-reduction [i] would yield (68, 70, large)-net in base 9, but