Best Known (81−57, 81, s)-Nets in Base 27
(81−57, 81, 114)-Net over F27 — Constructive and digital
Digital (24, 81, 114)-net over F27, using
- t-expansion [i] based on digital (23, 81, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(81−57, 81, 116)-Net in Base 27 — Constructive
(24, 81, 116)-net in base 27, using
- 7 times m-reduction [i] based on (24, 88, 116)-net in base 27, using
- base change [i] based on digital (2, 66, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 66, 116)-net over F81, using
(81−57, 81, 208)-Net over F27 — Digital
Digital (24, 81, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
(81−57, 81, 5326)-Net in Base 27 — Upper bound on s
There is no (24, 81, 5327)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 80, 5327)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3 234731 429749 094860 752189 308095 737606 306682 391277 075975 590878 430455 308151 493792 886504 917142 394682 877869 979890 563625 > 2780 [i]