Best Known (135−68, 135, s)-Nets in Base 9
(135−68, 135, 165)-Net over F9 — Constructive and digital
Digital (67, 135, 165)-net over F9, using
- t-expansion [i] based on digital (64, 135, 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
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(135−68, 135, 245)-Net over F9 — Digital
Digital (67, 135, 245)-net over F9, using
(135−68, 135, 10385)-Net in Base 9 — Upper bound on s
There is no (67, 135, 10386)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 666 180302 068688 244890 251422 617250 987791 928889 751716 833348 773681 070091 339874 612564 213030 643365 273137 259971 521628 316297 552855 865825 > 9135 [i]