Best Known (24, 24+36, s)-Nets in Base 27
(24, 24+36, 114)-Net over F27 — Constructive and digital
Digital (24, 60, 114)-net over F27, using
- t-expansion [i] based on digital (23, 60, 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
(24, 24+36, 172)-Net in Base 27 — Constructive
(24, 60, 172)-net in base 27, using
- 8 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(24, 24+36, 208)-Net over F27 — Digital
Digital (24, 60, 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
(24, 24+36, 244)-Net in Base 27
(24, 60, 244)-net in base 27, using
- base change [i] based on digital (9, 45, 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
(24, 24+36, 17144)-Net in Base 27 — Upper bound on s
There is no (24, 60, 17145)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 76 180472 742635 402838 138473 752754 860471 387145 189020 622209 483104 594029 968517 602942 769353 > 2760 [i]