Best Known (35, 35+54, s)-Nets in Base 27
(35, 35+54, 128)-Net over F27 — Constructive and digital
Digital (35, 89, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 31, 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 (4, 58, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 31, 64)-net over F27, using
(35, 35+54, 172)-Net in Base 27 — Constructive
(35, 89, 172)-net in base 27, using
- t-expansion [i] based on (34, 89, 172)-net in base 27, using
- 19 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 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, 81, 172)-net over F81, using
- 19 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
(35, 35+54, 220)-Net over F27 — Digital
Digital (35, 89, 220)-net over F27, using
- t-expansion [i] based on digital (33, 89, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
(35, 35+54, 298)-Net in Base 27
(35, 89, 298)-net in base 27, using
- 3 times m-reduction [i] based on (35, 92, 298)-net in base 27, using
- base change [i] based on digital (12, 69, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 69, 298)-net over F81, using
(35, 35+54, 21945)-Net in Base 27 — Upper bound on s
There is no (35, 89, 21946)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 24 625787 592213 454212 351983 075168 390312 613716 957068 290018 021486 173651 468260 788520 272206 361573 405999 501690 567447 575205 752742 151921 > 2789 [i]