Best Known (97−72, 97, s)-Nets in Base 9
(97−72, 97, 78)-Net over F9 — Constructive and digital
Digital (25, 97, 78)-net over F9, using
- t-expansion [i] based on digital (22, 97, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(97−72, 97, 96)-Net over F9 — Digital
Digital (25, 97, 96)-net over F9, using
- net from sequence [i] based on digital (25, 95)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 25 and N(F) ≥ 96, using
(97−72, 97, 643)-Net in Base 9 — Upper bound on s
There is no (25, 97, 644)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 380 902759 188711 638644 892658 484615 362937 955573 890992 127918 933894 364961 971412 317717 002052 774785 > 997 [i]