Best Known (146−24, 146, s)-Nets in Base 9
(146−24, 146, 88576)-Net over F9 — Constructive and digital
Digital (122, 146, 88576)-net over F9, using
- net defined by OOA [i] based on linear OOA(9146, 88576, F9, 24, 24) (dual of [(88576, 24), 2125678, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9146, 1062912, F9, 24) (dual of [1062912, 1062766, 25]-code), using
- trace code [i] based on linear OA(8173, 531456, F81, 24) (dual of [531456, 531383, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [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(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-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(23) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(8173, 531456, F81, 24) (dual of [531456, 531383, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9146, 1062912, F9, 24) (dual of [1062912, 1062766, 25]-code), using
(146−24, 146, 1345041)-Net over F9 — Digital
Digital (122, 146, 1345041)-net over F9, using
(146−24, 146, large)-Net in Base 9 — Upper bound on s
There is no (122, 146, large)-net in base 9, because
- 22 times m-reduction [i] would yield (122, 124, large)-net in base 9, but