Best Known (81, 105, s)-Nets in Base 9
(81, 105, 1096)-Net over F9 — Constructive and digital
Digital (81, 105, 1096)-net over F9, using
- 91 times duplication [i] based on digital (80, 104, 1096)-net over F9, using
- net defined by OOA [i] based on linear OOA(9104, 1096, F9, 24, 24) (dual of [(1096, 24), 26200, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9104, 13152, F9, 24) (dual of [13152, 13048, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9104, 13156, F9, 24) (dual of [13156, 13052, 25]-code), using
- trace code [i] based on linear OA(8152, 6578, F81, 24) (dual of [6578, 6526, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(8152, 6578, F81, 24) (dual of [6578, 6526, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9104, 13156, F9, 24) (dual of [13156, 13052, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9104, 13152, F9, 24) (dual of [13152, 13048, 25]-code), using
- net defined by OOA [i] based on linear OOA(9104, 1096, F9, 24, 24) (dual of [(1096, 24), 26200, 25]-NRT-code), using
(81, 105, 1640)-Net in Base 9 — Constructive
(81, 105, 1640)-net in base 9, using
- base change [i] based on digital (46, 70, 1640)-net over F27, using
- net defined by OOA [i] based on linear OOA(2770, 1640, F27, 24, 24) (dual of [(1640, 24), 39290, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
- net defined by OOA [i] based on linear OOA(2770, 1640, F27, 24, 24) (dual of [(1640, 24), 39290, 25]-NRT-code), using
(81, 105, 26784)-Net over F9 — Digital
Digital (81, 105, 26784)-net over F9, using
(81, 105, large)-Net in Base 9 — Upper bound on s
There is no (81, 105, large)-net in base 9, because
- 22 times m-reduction [i] would yield (81, 83, large)-net in base 9, but