Best Known (42−18, 42, s)-Nets in Base 7
(42−18, 42, 106)-Net over F7 — Constructive and digital
Digital (24, 42, 106)-net over F7, using
- trace code for nets [i] based on digital (3, 21, 53)-net over F49, using
- net from sequence [i] based on digital (3, 52)-sequence over F49, using
(42−18, 42, 184)-Net over F7 — Digital
Digital (24, 42, 184)-net over F7, using
- trace code for nets [i] based on digital (3, 21, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(42−18, 42, 6067)-Net in Base 7 — Upper bound on s
There is no (24, 42, 6068)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 312283 075931 181253 186550 657992 670905 > 742 [i]