Best Known (121, 121+24, s)-Nets in Base 9
(121, 121+24, 88575)-Net over F9 — Constructive and digital
Digital (121, 145, 88575)-net over F9, using
- 91 times duplication [i] based on digital (120, 144, 88575)-net over F9, using
- net defined by OOA [i] based on linear OOA(9144, 88575, F9, 24, 24) (dual of [(88575, 24), 2125656, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9144, 1062900, F9, 24) (dual of [1062900, 1062756, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9144, 1062904, F9, 24) (dual of [1062904, 1062760, 25]-code), using
- trace code [i] based on linear OA(8172, 531452, F81, 24) (dual of [531452, 531380, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(8170, 531441, F81, 24) (dual of [531441, 531371, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-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(23) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(8172, 531452, F81, 24) (dual of [531452, 531380, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9144, 1062904, F9, 24) (dual of [1062904, 1062760, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9144, 1062900, F9, 24) (dual of [1062900, 1062756, 25]-code), using
- net defined by OOA [i] based on linear OOA(9144, 88575, F9, 24, 24) (dual of [(88575, 24), 2125656, 25]-NRT-code), using
(121, 121+24, 1222495)-Net over F9 — Digital
Digital (121, 145, 1222495)-net over F9, using
(121, 121+24, large)-Net in Base 9 — Upper bound on s
There is no (121, 145, large)-net in base 9, because
- 22 times m-reduction [i] would yield (121, 123, large)-net in base 9, but