Best Known (50, 75, s)-Nets in Base 7
(50, 75, 200)-Net over F7 — Constructive and digital
Digital (50, 75, 200)-net over F7, using
- 71 times duplication [i] based on digital (49, 74, 200)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 12, 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
- trace code for nets [i] based on digital (0, 12, 50)-net over F49, using
- digital (25, 50, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 25, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- trace code for nets [i] based on digital (0, 25, 50)-net over F49, using
- digital (12, 24, 100)-net over F7, using
- (u, u+v)-construction [i] based on
(50, 75, 727)-Net over F7 — Digital
Digital (50, 75, 727)-net over F7, using
(50, 75, 143425)-Net in Base 7 — Upper bound on s
There is no (50, 75, 143426)-net in base 7, because
- 1 times m-reduction [i] would yield (50, 74, 143426)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 344 576129 017662 035908 840707 916411 771637 015783 735164 123006 694041 > 774 [i]