Best Known (78−56, 78, s)-Nets in Base 9
(78−56, 78, 78)-Net over F9 — Constructive and digital
Digital (22, 78, 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
(78−56, 78, 88)-Net over F9 — Digital
Digital (22, 78, 88)-net over F9, using
- t-expansion [i] based on digital (21, 78, 88)-net over F9, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
(78−56, 78, 626)-Net in Base 9 — Upper bound on s
There is no (22, 78, 627)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 280 991267 848255 060949 760883 721426 867206 795590 883887 563295 683780 040686 210977 > 978 [i]