Best Known (52, 52+42, s)-Nets in Base 27
(52, 52+42, 222)-Net over F27 — Constructive and digital
Digital (52, 94, 222)-net over F27, using
- 1 times m-reduction [i] based on digital (52, 95, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 18, 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 (6, 27, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 50, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 18, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(52, 52+42, 370)-Net in Base 27 — Constructive
(52, 94, 370)-net in base 27, using
- t-expansion [i] based on (43, 94, 370)-net in base 27, using
- 14 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- 14 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(52, 52+42, 1208)-Net over F27 — Digital
Digital (52, 94, 1208)-net over F27, using
(52, 52+42, 852256)-Net in Base 27 — Upper bound on s
There is no (52, 94, 852257)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 353 341108 239101 442988 099999 947310 114335 640709 031806 609907 578901 823379 372846 966639 391351 939303 004057 550329 086715 861037 488234 996206 216939 > 2794 [i]