Best Known (84−62, 84, s)-Nets in Base 9
(84−62, 84, 78)-Net over F9 — Constructive and digital
Digital (22, 84, 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
(84−62, 84, 88)-Net over F9 — Digital
Digital (22, 84, 88)-net over F9, using
- t-expansion [i] based on digital (21, 84, 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
(84−62, 84, 579)-Net in Base 9 — Upper bound on s
There is no (22, 84, 580)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 149 375667 928277 646567 288576 481444 721069 356339 746440 863480 878140 376967 386740 771937 > 984 [i]