Best Known (81, 81+16, s)-Nets in Base 9
(81, 81+16, 132863)-Net over F9 — Constructive and digital
Digital (81, 97, 132863)-net over F9, using
- 91 times duplication [i] based on digital (80, 96, 132863)-net over F9, using
- net defined by OOA [i] based on linear OOA(996, 132863, F9, 16, 16) (dual of [(132863, 16), 2125712, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(996, 1062904, F9, 16) (dual of [1062904, 1062808, 17]-code), using
- trace code [i] based on linear OA(8148, 531452, F81, 16) (dual of [531452, 531404, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(15) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(8148, 531452, F81, 16) (dual of [531452, 531404, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(996, 1062904, F9, 16) (dual of [1062904, 1062808, 17]-code), using
- net defined by OOA [i] based on linear OOA(996, 132863, F9, 16, 16) (dual of [(132863, 16), 2125712, 17]-NRT-code), using
(81, 81+16, 1189728)-Net over F9 — Digital
Digital (81, 97, 1189728)-net over F9, using
(81, 81+16, large)-Net in Base 9 — Upper bound on s
There is no (81, 97, large)-net in base 9, because
- 14 times m-reduction [i] would yield (81, 83, large)-net in base 9, but