Best Known (52, 52+34, s)-Nets in Base 27
(52, 52+34, 258)-Net over F27 — Constructive and digital
Digital (52, 86, 258)-net over F27, using
- 1 times m-reduction [i] based on digital (52, 87, 258)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 18, 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 (7, 24, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (10, 45, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (7, 18, 82)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(52, 52+34, 418)-Net in Base 27 — Constructive
(52, 86, 418)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (2, 19, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- (33, 67, 370)-net in base 27, using
- 1 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- base change [i] based on digital (16, 51, 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, 51, 370)-net over F81, using
- 1 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- digital (2, 19, 48)-net over F27, using
(52, 52+34, 2737)-Net over F27 — Digital
Digital (52, 86, 2737)-net over F27, using
(52, 52+34, 4808258)-Net in Base 27 — Upper bound on s
There is no (52, 86, 4808259)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1251 080319 164696 099241 228671 355728 232808 820223 152257 228388 712108 019733 796049 159900 463782 479215 446407 012525 574312 329135 020975 > 2786 [i]