Best Known (27, 67, s)-Nets in Base 27
(27, 67, 116)-Net over F27 — Constructive and digital
Digital (27, 67, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 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, 44, 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, 23, 52)-net over F27, using
(27, 67, 172)-Net in Base 27 — Constructive
(27, 67, 172)-net in base 27, using
- 13 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, 67, 208)-Net over F27 — Digital
Digital (27, 67, 208)-net over F27, using
- t-expansion [i] based on digital (24, 67, 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, 67, 244)-Net in Base 27
(27, 67, 244)-net in base 27, using
- 5 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, 67, 19914)-Net in Base 27 — Upper bound on s
There is no (27, 67, 19915)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 796940 281676 156574 416241 215406 473666 429412 182222 110766 818216 762805 176853 456403 111006 570705 320409 > 2767 [i]