Best Known (159, 206, s)-Nets in Base 3
(159, 206, 600)-Net over F3 — Constructive and digital
Digital (159, 206, 600)-net over F3, using
- 32 times duplication [i] based on digital (157, 204, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 51, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 51, 150)-net over F81, using
(159, 206, 1255)-Net over F3 — Digital
Digital (159, 206, 1255)-net over F3, using
(159, 206, 84316)-Net in Base 3 — Upper bound on s
There is no (159, 206, 84317)-net in base 3, because
- 1 times m-reduction [i] would yield (159, 205, 84317)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 64 551848 122885 293508 753068 412079 532823 415593 363018 002673 968726 889702 342854 204874 290600 471150 255483 > 3205 [i]