Best Known (137−73, 137, s)-Nets in Base 9
(137−73, 137, 165)-Net over F9 — Constructive and digital
Digital (64, 137, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
(137−73, 137, 196)-Net over F9 — Digital
Digital (64, 137, 196)-net over F9, using
(137−73, 137, 7165)-Net in Base 9 — Upper bound on s
There is no (64, 137, 7166)-net in base 9, because
- 1 times m-reduction [i] would yield (64, 136, 7166)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 6005 535830 260384 424177 871399 153150 726590 617772 788627 108683 147360 709848 549603 260975 511578 100873 720983 456367 576791 783456 563632 085825 > 9136 [i]