Best Known (60, 78, s)-Nets in Base 9
(60, 78, 1461)-Net over F9 — Constructive and digital
Digital (60, 78, 1461)-net over F9, using
- net defined by OOA [i] based on linear OOA(978, 1461, F9, 18, 18) (dual of [(1461, 18), 26220, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(978, 13149, F9, 18) (dual of [13149, 13071, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(978, 13150, F9, 18) (dual of [13150, 13072, 19]-code), using
- trace code [i] based on linear OA(8139, 6575, F81, 18) (dual of [6575, 6536, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [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(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(8139, 6575, F81, 18) (dual of [6575, 6536, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(978, 13150, F9, 18) (dual of [13150, 13072, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(978, 13149, F9, 18) (dual of [13149, 13071, 19]-code), using
(60, 78, 2187)-Net in Base 9 — Constructive
(60, 78, 2187)-net in base 9, using
- base change [i] based on digital (34, 52, 2187)-net over F27, using
- net defined by OOA [i] based on linear OOA(2752, 2187, F27, 18, 18) (dual of [(2187, 18), 39314, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using
- net defined by OOA [i] based on linear OOA(2752, 2187, F27, 18, 18) (dual of [(2187, 18), 39314, 19]-NRT-code), using
(60, 78, 21444)-Net over F9 — Digital
Digital (60, 78, 21444)-net over F9, using
(60, 78, large)-Net in Base 9 — Upper bound on s
There is no (60, 78, large)-net in base 9, because
- 16 times m-reduction [i] would yield (60, 62, large)-net in base 9, but