Best Known (64, 64+65, s)-Nets in Base 9
(64, 64+65, 165)-Net over F9 — Constructive and digital
Digital (64, 129, 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
(64, 64+65, 236)-Net over F9 — Digital
Digital (64, 129, 236)-net over F9, using
(64, 64+65, 10470)-Net in Base 9 — Upper bound on s
There is no (64, 129, 10471)-net in base 9, because
- 1 times m-reduction [i] would yield (64, 128, 10471)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 139 370762 316292 539923 397858 073555 152253 892896 880896 559404 991624 575300 056511 173156 769868 574206 325561 320303 992554 070338 582273 > 9128 [i]