Best Known (111−18, 111, s)-Nets in Base 9
(111−18, 111, 118101)-Net over F9 — Constructive and digital
Digital (93, 111, 118101)-net over F9, using
- 91 times duplication [i] based on digital (92, 110, 118101)-net over F9, using
- net defined by OOA [i] based on linear OOA(9110, 118101, F9, 18, 18) (dual of [(118101, 18), 2125708, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9110, 1062909, F9, 18) (dual of [1062909, 1062799, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9110, 1062912, F9, 18) (dual of [1062912, 1062802, 19]-code), using
- trace code [i] based on linear OA(8155, 531456, F81, 18) (dual of [531456, 531401, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(17) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(8155, 531456, F81, 18) (dual of [531456, 531401, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9110, 1062912, F9, 18) (dual of [1062912, 1062802, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(9110, 1062909, F9, 18) (dual of [1062909, 1062799, 19]-code), using
- net defined by OOA [i] based on linear OOA(9110, 118101, F9, 18, 18) (dual of [(118101, 18), 2125708, 19]-NRT-code), using
(111−18, 111, 1525808)-Net over F9 — Digital
Digital (93, 111, 1525808)-net over F9, using
(111−18, 111, large)-Net in Base 9 — Upper bound on s
There is no (93, 111, large)-net in base 9, because
- 16 times m-reduction [i] would yield (93, 95, large)-net in base 9, but