Best Known (70, 84, s)-Nets in Base 9
(70, 84, 151843)-Net over F9 — Constructive and digital
Digital (70, 84, 151843)-net over F9, using
- net defined by OOA [i] based on linear OOA(984, 151843, F9, 14, 14) (dual of [(151843, 14), 2125718, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(984, 1062901, F9, 14) (dual of [1062901, 1062817, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(984, 1062904, F9, 14) (dual of [1062904, 1062820, 15]-code), using
- trace code [i] based on linear OA(8142, 531452, F81, 14) (dual of [531452, 531410, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 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(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(8142, 531452, F81, 14) (dual of [531452, 531410, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(984, 1062904, F9, 14) (dual of [1062904, 1062820, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(984, 1062901, F9, 14) (dual of [1062901, 1062817, 15]-code), using
(70, 84, 1062904)-Net over F9 — Digital
Digital (70, 84, 1062904)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(984, 1062904, F9, 14) (dual of [1062904, 1062820, 15]-code), using
- trace code [i] based on linear OA(8142, 531452, F81, 14) (dual of [531452, 531410, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 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(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(8142, 531452, F81, 14) (dual of [531452, 531410, 15]-code), using
(70, 84, large)-Net in Base 9 — Upper bound on s
There is no (70, 84, large)-net in base 9, because
- 12 times m-reduction [i] would yield (70, 72, large)-net in base 9, but