Best Known (83, 83+26, s)-Nets in Base 9
(83, 83+26, 1011)-Net over F9 — Constructive and digital
Digital (83, 109, 1011)-net over F9, using
- 91 times duplication [i] based on digital (82, 108, 1011)-net over F9, using
- net defined by OOA [i] based on linear OOA(9108, 1011, F9, 26, 26) (dual of [(1011, 26), 26178, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9108, 13143, F9, 26) (dual of [13143, 13035, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9108, 13144, F9, 26) (dual of [13144, 13036, 27]-code), using
- trace code [i] based on linear OA(8154, 6572, F81, 26) (dual of [6572, 6518, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-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(25) ⊂ Ce(21) [i] based on
- trace code [i] based on linear OA(8154, 6572, F81, 26) (dual of [6572, 6518, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9108, 13144, F9, 26) (dual of [13144, 13036, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9108, 13143, F9, 26) (dual of [13143, 13035, 27]-code), using
- net defined by OOA [i] based on linear OOA(9108, 1011, F9, 26, 26) (dual of [(1011, 26), 26178, 27]-NRT-code), using
(83, 83+26, 18422)-Net over F9 — Digital
Digital (83, 109, 18422)-net over F9, using
(83, 83+26, large)-Net in Base 9 — Upper bound on s
There is no (83, 109, large)-net in base 9, because
- 24 times m-reduction [i] would yield (83, 85, large)-net in base 9, but