Best Known (33, 33+52, s)-Nets in Base 27
(33, 33+52, 116)-Net over F27 — Constructive and digital
Digital (33, 85, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 29, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 56, 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 (3, 29, 52)-net over F27, using
(33, 33+52, 172)-Net in Base 27 — Constructive
(33, 85, 172)-net in base 27, using
- 19 times m-reduction [i] based on (33, 104, 172)-net in base 27, using
- base change [i] based on digital (7, 78, 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, 78, 172)-net over F81, using
(33, 33+52, 220)-Net over F27 — Digital
Digital (33, 85, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
(33, 33+52, 244)-Net in Base 27
(33, 85, 244)-net in base 27, using
- 11 times m-reduction [i] based on (33, 96, 244)-net in base 27, using
- base change [i] based on digital (9, 72, 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, 72, 244)-net over F81, using
(33, 33+52, 19385)-Net in Base 27 — Upper bound on s
There is no (33, 85, 19386)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 46 370389 047143 395002 565136 246764 405452 427400 544189 036278 606012 112209 878587 070356 044937 444011 275625 682509 253333 982779 928789 > 2785 [i]