Best Known (18, 18+35, s)-Nets in Base 49
(18, 18+35, 101)-Net over F49 — Constructive and digital
Digital (18, 53, 101)-net over F49, using
- (u, u+v)-construction [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
- digital (1, 36, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 17, 50)-net over F49, using
(18, 18+35, 116)-Net over F49 — Digital
Digital (18, 53, 116)-net over F49, using
(18, 18+35, 22108)-Net in Base 49 — Upper bound on s
There is no (18, 53, 22109)-net in base 49, because
- 1 times m-reduction [i] would yield (18, 52, 22109)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 7771 345654 386850 575293 143028 163051 633468 313671 950334 563876 233974 512370 116974 647467 221105 > 4952 [i]