Best Known (27, 27+44, s)-Nets in Base 27
(27, 27+44, 114)-Net over F27 — Constructive and digital
Digital (27, 71, 114)-net over F27, using
- t-expansion [i] based on digital (23, 71, 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
(27, 27+44, 172)-Net in Base 27 — Constructive
(27, 71, 172)-net in base 27, using
- 9 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 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, 60, 172)-net over F81, using
(27, 27+44, 208)-Net over F27 — Digital
Digital (27, 71, 208)-net over F27, using
- t-expansion [i] based on digital (24, 71, 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
(27, 27+44, 244)-Net in Base 27
(27, 71, 244)-net in base 27, using
- 1 times m-reduction [i] based on (27, 72, 244)-net in base 27, using
- base change [i] based on digital (9, 54, 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, 54, 244)-net over F81, using
(27, 27+44, 14485)-Net in Base 27 — Upper bound on s
There is no (27, 71, 14486)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 423636 060009 845151 055377 647315 106226 310673 267699 354655 843600 984030 221471 087678 650196 683647 791991 601301 > 2771 [i]