Best Known (108−18, 108, s)-Nets in Base 9
(108−18, 108, 118100)-Net over F9 — Constructive and digital
Digital (90, 108, 118100)-net over F9, using
- net defined by OOA [i] based on linear OOA(9108, 118100, F9, 18, 18) (dual of [(118100, 18), 2125692, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9108, 1062900, F9, 18) (dual of [1062900, 1062792, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9108, 1062904, F9, 18) (dual of [1062904, 1062796, 19]-code), using
- trace code [i] based on linear OA(8154, 531452, F81, 18) (dual of [531452, 531398, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [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(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(17) ⊂ Ce(14) [i] based on
- trace code [i] based on linear OA(8154, 531452, F81, 18) (dual of [531452, 531398, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9108, 1062904, F9, 18) (dual of [1062904, 1062796, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(9108, 1062900, F9, 18) (dual of [1062900, 1062792, 19]-code), using
(108−18, 108, 1062904)-Net over F9 — Digital
Digital (90, 108, 1062904)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9108, 1062904, F9, 18) (dual of [1062904, 1062796, 19]-code), using
- trace code [i] based on linear OA(8154, 531452, F81, 18) (dual of [531452, 531398, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [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(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(17) ⊂ Ce(14) [i] based on
- trace code [i] based on linear OA(8154, 531452, F81, 18) (dual of [531452, 531398, 19]-code), using
(108−18, 108, large)-Net in Base 9 — Upper bound on s
There is no (90, 108, large)-net in base 9, because
- 16 times m-reduction [i] would yield (90, 92, large)-net in base 9, but