Best Known (45, 45+45, s)-Nets in Base 7
(45, 45+45, 100)-Net over F7 — Constructive and digital
Digital (45, 90, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 45, 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
(45, 45+45, 139)-Net over F7 — Digital
Digital (45, 90, 139)-net over F7, using
(45, 45+45, 3944)-Net in Base 7 — Upper bound on s
There is no (45, 90, 3945)-net in base 7, because
- 1 times m-reduction [i] would yield (45, 89, 3945)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 1643 631999 939480 506338 920319 911271 411165 061054 230588 875283 336787 744991 194977 > 789 [i]