Best Known (80−49, 80, s)-Nets in Base 27
(80−49, 80, 116)-Net over F27 — Constructive and digital
Digital (31, 80, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 27, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 53, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (3, 27, 52)-net over F27, using
(80−49, 80, 172)-Net in Base 27 — Constructive
(31, 80, 172)-net in base 27, using
- 16 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
(80−49, 80, 208)-Net over F27 — Digital
Digital (31, 80, 208)-net over F27, using
- t-expansion [i] based on digital (24, 80, 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
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(80−49, 80, 244)-Net in Base 27
(31, 80, 244)-net in base 27, using
- 8 times m-reduction [i] based on (31, 88, 244)-net in base 27, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
(80−49, 80, 19394)-Net in Base 27 — Upper bound on s
There is no (31, 80, 19395)-net in base 27, because
- 1 times m-reduction [i] would yield (31, 79, 19395)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 119641 727885 612230 509185 382760 915269 864345 993834 114224 709953 861348 505527 294326 149078 901775 168858 452608 913241 457297 > 2779 [i]