Best Known (59, 59+49, s)-Nets in Base 27
(59, 59+49, 234)-Net over F27 — Constructive and digital
Digital (59, 108, 234)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 22, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 30, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (7, 56, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (6, 22, 76)-net over F27, using
(59, 59+49, 370)-Net in Base 27 — Constructive
(59, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
(59, 59+49, 1222)-Net over F27 — Digital
Digital (59, 108, 1222)-net over F27, using
(59, 59+49, 907570)-Net in Base 27 — Upper bound on s
There is no (59, 108, 907571)-net in base 27, because
- 1 times m-reduction [i] would yield (59, 107, 907571)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1431 963668 327497 690592 587447 396107 125791 243409 311616 985903 197999 054532 507804 717000 968872 493792 210538 344903 760212 527910 604037 530694 754093 081233 592349 722001 > 27107 [i]