Best Known (42−25, 42, s)-Nets in Base 7
(42−25, 42, 25)-Net over F7 — Constructive and digital
Digital (17, 42, 25)-net over F7, using
- net from sequence [i] based on digital (17, 24)-sequence over F7, using
(42−25, 42, 48)-Net over F7 — Digital
Digital (17, 42, 48)-net over F7, using
- t-expansion [i] based on digital (13, 42, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
(42−25, 42, 672)-Net in Base 7 — Upper bound on s
There is no (17, 42, 673)-net in base 7, because
- 1 times m-reduction [i] would yield (17, 41, 673)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 44792 472380 788656 545368 673832 851233 > 741 [i]