Best Known (60, 121, s)-Nets in Base 3
(60, 121, 56)-Net over F3 — Constructive and digital
Digital (60, 121, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 45, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (15, 76, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 45, 28)-net over F3, using
(60, 121, 64)-Net over F3 — Digital
Digital (60, 121, 64)-net over F3, using
- t-expansion [i] based on digital (49, 121, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(60, 121, 459)-Net in Base 3 — Upper bound on s
There is no (60, 121, 460)-net in base 3, because
- 1 times m-reduction [i] would yield (60, 120, 460)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1908 280147 039473 442403 616164 290798 837145 246330 637632 176905 > 3120 [i]