Best Known (67, 83, s)-Nets in Base 9
(67, 83, 7411)-Net over F9 — Constructive and digital
Digital (67, 83, 7411)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- digital (55, 71, 7381)-net over F9, using
- net defined by OOA [i] based on linear OOA(971, 7381, F9, 16, 16) (dual of [(7381, 16), 118025, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(971, 59048, F9, 16) (dual of [59048, 58977, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(971, 59048, F9, 16) (dual of [59048, 58977, 17]-code), using
- net defined by OOA [i] based on linear OOA(971, 7381, F9, 16, 16) (dual of [(7381, 16), 118025, 17]-NRT-code), using
- digital (4, 12, 30)-net over F9, using
(67, 83, 153052)-Net over F9 — Digital
Digital (67, 83, 153052)-net over F9, using
(67, 83, large)-Net in Base 9 — Upper bound on s
There is no (67, 83, large)-net in base 9, because
- 14 times m-reduction [i] would yield (67, 69, large)-net in base 9, but