Best Known (73, 73+18, s)-Nets in Base 9
(73, 73+18, 6581)-Net over F9 — Constructive and digital
Digital (73, 91, 6581)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (62, 80, 6561)-net over F9, using
- net defined by OOA [i] based on linear OOA(980, 6561, F9, 18, 18) (dual of [(6561, 18), 118018, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(980, 59049, F9, 18) (dual of [59049, 58969, 19]-code), using
- 1 times truncation [i] based on linear OA(981, 59050, F9, 19) (dual of [59050, 58969, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(981, 59050, F9, 19) (dual of [59050, 58969, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(980, 59049, F9, 18) (dual of [59049, 58969, 19]-code), using
- net defined by OOA [i] based on linear OOA(980, 6561, F9, 18, 18) (dual of [(6561, 18), 118018, 19]-NRT-code), using
- digital (2, 11, 20)-net over F9, using
(73, 73+18, 115051)-Net over F9 — Digital
Digital (73, 91, 115051)-net over F9, using
(73, 73+18, large)-Net in Base 9 — Upper bound on s
There is no (73, 91, large)-net in base 9, because
- 16 times m-reduction [i] would yield (73, 75, large)-net in base 9, but