Best Known (3, 3+17, s)-Nets in Base 7
(3, 3+17, 11)-Net over F7 — Constructive and digital
Digital (3, 20, 11)-net over F7, using
- net from sequence [i] based on digital (3, 10)-sequence over F7, using
- Niederreiter sequence (Bratley–Fox–Niederreiter implementation) with equidistant coordinate [i]
(3, 3+17, 20)-Net over F7 — Digital
Digital (3, 20, 20)-net over F7, using
- net from sequence [i] based on digital (3, 19)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 3 and N(F) ≥ 20, using
(3, 3+17, 59)-Net in Base 7 — Upper bound on s
There is no (3, 20, 60)-net in base 7, because
- 1 times m-reduction [i] would yield (3, 19, 60)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 12810 431610 580033 > 719 [i]