Best Known (32, 32+53, s)-Nets in Base 27
(32, 32+53, 114)-Net over F27 — Constructive and digital
Digital (32, 85, 114)-net over F27, using
- t-expansion [i] based on digital (23, 85, 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
(32, 32+53, 172)-Net in Base 27 — Constructive
(32, 85, 172)-net in base 27, using
- 15 times m-reduction [i] based on (32, 100, 172)-net in base 27, using
- base change [i] based on digital (7, 75, 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, 75, 172)-net over F81, using
(32, 32+53, 208)-Net over F27 — Digital
Digital (32, 85, 208)-net over F27, using
- t-expansion [i] based on digital (24, 85, 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
(32, 32+53, 244)-Net in Base 27
(32, 85, 244)-net in base 27, using
- 7 times m-reduction [i] based on (32, 92, 244)-net in base 27, using
- base change [i] based on digital (9, 69, 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, 69, 244)-net over F81, using
(32, 32+53, 17075)-Net in Base 27 — Upper bound on s
There is no (32, 85, 17076)-net in base 27, because
- 1 times m-reduction [i] would yield (32, 84, 17076)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 716523 283513 433272 328703 585995 291281 118719 199010 123093 403589 222780 214011 055452 243698 784836 952176 819320 877072 423106 591705 > 2784 [i]