Best Known (68, 137, s)-Nets in Base 5
(68, 137, 88)-Net over F5 — Constructive and digital
Digital (68, 137, 88)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 37, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- digital (31, 100, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- digital (3, 37, 16)-net over F5, using
(68, 137, 132)-Net over F5 — Digital
Digital (68, 137, 132)-net over F5, using
- t-expansion [i] based on digital (67, 137, 132)-net over F5, using
- net from sequence [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- net from sequence [i] based on digital (67, 131)-sequence over F5, using
(68, 137, 2090)-Net in Base 5 — Upper bound on s
There is no (68, 137, 2091)-net in base 5, because
- 1 times m-reduction [i] would yield (68, 136, 2091)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 116593 693630 737415 253542 415926 703213 531133 362779 003657 593980 440388 293850 507340 611202 531356 598265 > 5136 [i]