Best Known (31, 31+56, s)-Nets in Base 27
(31, 31+56, 114)-Net over F27 — Constructive and digital
Digital (31, 87, 114)-net over F27, using
- t-expansion [i] based on digital (23, 87, 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
(31, 31+56, 172)-Net in Base 27 — Constructive
(31, 87, 172)-net in base 27, using
- 9 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 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, 72, 172)-net over F81, using
(31, 31+56, 208)-Net over F27 — Digital
Digital (31, 87, 208)-net over F27, using
- t-expansion [i] based on digital (24, 87, 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
(31, 31+56, 244)-Net in Base 27
(31, 87, 244)-net in base 27, using
- 1 times m-reduction [i] based on (31, 88, 244)-net in base 27, using
- base change [i] based on digital (9, 66, 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, 66, 244)-net over F81, using
(31, 31+56, 12160)-Net in Base 27 — Upper bound on s
There is no (31, 87, 12161)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 33792 192795 478390 122299 955620 126893 195597 916320 166504 003622 982623 809064 326843 993668 738311 724534 076537 505484 741614 463563 306129 > 2787 [i]