Best Known (80−58, 80, s)-Nets in Base 9
(80−58, 80, 78)-Net over F9 — Constructive and digital
Digital (22, 80, 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
(80−58, 80, 88)-Net over F9 — Digital
Digital (22, 80, 88)-net over F9, using
- t-expansion [i] based on digital (21, 80, 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
(80−58, 80, 608)-Net in Base 9 — Upper bound on s
There is no (22, 80, 609)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 22561 698183 757082 535002 512203 492531 759827 487275 501453 010103 231900 749994 221929 > 980 [i]