Best Known (29, 29+45, s)-Nets in Base 27
(29, 29+45, 116)-Net over F27 — Constructive and digital
Digital (29, 74, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 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, 49, 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, 25, 52)-net over F27, using
(29, 29+45, 172)-Net in Base 27 — Constructive
(29, 74, 172)-net in base 27, using
- 14 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(29, 29+45, 208)-Net over F27 — Digital
Digital (29, 74, 208)-net over F27, using
- t-expansion [i] based on digital (24, 74, 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
(29, 29+45, 244)-Net in Base 27
(29, 74, 244)-net in base 27, using
- 6 times m-reduction [i] based on (29, 80, 244)-net in base 27, using
- base change [i] based on digital (9, 60, 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, 60, 244)-net over F81, using
(29, 29+45, 19550)-Net in Base 27 — Upper bound on s
There is no (29, 74, 19551)-net in base 27, because
- 1 times m-reduction [i] would yield (29, 73, 19551)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 308 963373 072991 908214 105430 185514 599825 292936 632421 164151 727965 382393 191559 946946 367524 183888 046402 911109 > 2773 [i]