Best Known (90−17, 90, s)-Nets in Base 9
(90−17, 90, 7415)-Net over F9 — Constructive and digital
Digital (73, 90, 7415)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (59, 76, 7381)-net over F9, using
- net defined by OOA [i] based on linear OOA(976, 7381, F9, 17, 17) (dual of [(7381, 17), 125401, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- net defined by OOA [i] based on linear OOA(976, 7381, F9, 17, 17) (dual of [(7381, 17), 125401, 18]-NRT-code), using
- digital (6, 14, 34)-net over F9, using
(90−17, 90, 7419)-Net in Base 9 — Constructive
(73, 90, 7419)-net in base 9, using
- (u, u+v)-construction [i] based on
- (6, 14, 38)-net in base 9, using
- 1 times m-reduction [i] based on (6, 15, 38)-net in base 9, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
- 1 times m-reduction [i] based on (6, 15, 38)-net in base 9, using
- digital (59, 76, 7381)-net over F9, using
- net defined by OOA [i] based on linear OOA(976, 7381, F9, 17, 17) (dual of [(7381, 17), 125401, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- net defined by OOA [i] based on linear OOA(976, 7381, F9, 17, 17) (dual of [(7381, 17), 125401, 18]-NRT-code), using
- (6, 14, 38)-net in base 9, using
(90−17, 90, 198189)-Net over F9 — Digital
Digital (73, 90, 198189)-net over F9, using
(90−17, 90, large)-Net in Base 9 — Upper bound on s
There is no (73, 90, large)-net in base 9, because
- 15 times m-reduction [i] would yield (73, 75, large)-net in base 9, but