Best Known (33, 33+57, s)-Nets in Base 27
(33, 33+57, 114)-Net over F27 — Constructive and digital
Digital (33, 90, 114)-net over F27, using
- t-expansion [i] based on digital (23, 90, 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
(33, 33+57, 172)-Net in Base 27 — Constructive
(33, 90, 172)-net in base 27, using
- 14 times m-reduction [i] based on (33, 104, 172)-net in base 27, using
- base change [i] based on digital (7, 78, 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, 78, 172)-net over F81, using
(33, 33+57, 220)-Net over F27 — Digital
Digital (33, 90, 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
(33, 33+57, 244)-Net in Base 27
(33, 90, 244)-net in base 27, using
- 6 times m-reduction [i] based on (33, 96, 244)-net in base 27, using
- base change [i] based on digital (9, 72, 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, 72, 244)-net over F81, using
(33, 33+57, 15392)-Net in Base 27 — Upper bound on s
There is no (33, 90, 15393)-net in base 27, because
- 1 times m-reduction [i] would yield (33, 89, 15393)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 24 641782 890156 697791 899888 858221 138676 554325 473467 242849 259638 797929 792163 704768 588572 285183 989066 220109 398680 821615 190641 833361 > 2789 [i]