Best Known (24, 24+33, s)-Nets in Base 27
(24, 24+33, 128)-Net over F27 — Constructive and digital
Digital (24, 57, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 20, 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, 37, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 20, 64)-net over F27, using
(24, 24+33, 172)-Net in Base 27 — Constructive
(24, 57, 172)-net in base 27, using
- 11 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+33, 208)-Net over F27 — Digital
Digital (24, 57, 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+33, 244)-Net in Base 27
(24, 57, 244)-net in base 27, using
- 3 times m-reduction [i] based on (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
- base change [i] based on digital (9, 45, 244)-net over F81, using
(24, 24+33, 26742)-Net in Base 27 — Upper bound on s
There is no (24, 57, 26743)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 56, 26743)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 143 358727 545317 784208 395898 614449 796609 364295 867276 570771 526359 241912 974512 697697 > 2756 [i]