Best Known (42−21, 42, s)-Nets in Base 7
(42−21, 42, 100)-Net over F7 — Constructive and digital
Digital (21, 42, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 21, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
(42−21, 42, 2195)-Net in Base 7 — Upper bound on s
There is no (21, 42, 2196)-net in base 7, because
- 1 times m-reduction [i] would yield (21, 41, 2196)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 44693 030056 086220 143403 004851 760761 > 741 [i]