Best Known (72, 107, s)-Nets in Base 7
(72, 107, 202)-Net over F7 — Constructive and digital
Digital (72, 107, 202)-net over F7, using
- 71 times duplication [i] based on digital (71, 106, 202)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (17, 34, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 17, 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, 17, 50)-net over F49, using
- digital (37, 72, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 36, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- trace code for nets [i] based on digital (1, 36, 51)-net over F49, using
- digital (17, 34, 100)-net over F7, using
- (u, u+v)-construction [i] based on
(72, 107, 1047)-Net over F7 — Digital
Digital (72, 107, 1047)-net over F7, using
(72, 107, 222437)-Net in Base 7 — Upper bound on s
There is no (72, 107, 222438)-net in base 7, because
- 1 times m-reduction [i] would yield (72, 106, 222438)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 380552 856218 226130 736196 218533 199731 436003 894259 794406 635488 042907 474674 745009 793778 963909 > 7106 [i]