Best Known (7, 7+35, s)-Nets in Base 25
(7, 7+35, 66)-Net over F25 — Constructive and digital
Digital (7, 42, 66)-net over F25, using
- t-expansion [i] based on digital (4, 42, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
(7, 7+35, 694)-Net in Base 25 — Upper bound on s
There is no (7, 42, 695)-net in base 25, because
- 1 times m-reduction [i] would yield (7, 41, 695)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2079 371729 539375 171109 275574 158634 827521 782885 037127 392169 > 2541 [i]