Best Known (42, 42+39, s)-Nets in Base 9
(42, 42+39, 200)-Net over F9 — Constructive and digital
Digital (42, 81, 200)-net over F9, using
- 1 times m-reduction [i] based on digital (42, 82, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 41, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 41, 100)-net over F81, using
(42, 42+39, 10315)-Net in Base 9 — Upper bound on s
There is no (42, 81, 10316)-net in base 9, because
- 1 times m-reduction [i] would yield (42, 80, 10316)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21848 473869 527325 768058 298848 269457 665815 505241 592268 042237 418365 790084 785057 > 980 [i]