Best Known (72, 72+17, s)-Nets in Base 9
(72, 72+17, 7413)-Net over F9 — Constructive and digital
Digital (72, 89, 7413)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-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 (5, 13, 32)-net over F9, using
(72, 72+17, 172760)-Net over F9 — Digital
Digital (72, 89, 172760)-net over F9, using
(72, 72+17, large)-Net in Base 9 — Upper bound on s
There is no (72, 89, large)-net in base 9, because
- 15 times m-reduction [i] would yield (72, 74, large)-net in base 9, but