Best Known (161, 161+59, s)-Nets in Base 3
(161, 161+59, 288)-Net over F3 — Constructive and digital
Digital (161, 220, 288)-net over F3, using
- 5 times m-reduction [i] based on digital (161, 225, 288)-net over F3, using
- trace code for nets [i] based on digital (11, 75, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- trace code for nets [i] based on digital (11, 75, 96)-net over F27, using
(161, 161+59, 705)-Net over F3 — Digital
Digital (161, 220, 705)-net over F3, using
(161, 161+59, 23369)-Net in Base 3 — Upper bound on s
There is no (161, 220, 23370)-net in base 3, because
- 1 times m-reduction [i] would yield (161, 219, 23370)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 308 870012 896955 559427 885348 410892 864698 497933 778160 780208 970903 200265 666441 856002 124298 079440 068063 985021 > 3219 [i]