Best Known (61, 61+40, s)-Nets in Base 27
(61, 61+40, 272)-Net over F27 — Constructive and digital
Digital (61, 101, 272)-net over F27, using
- 1 times m-reduction [i] based on digital (61, 102, 272)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (8, 21, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 30, 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 (10, 51, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27 (see above)
- digital (8, 21, 84)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(61, 61+40, 446)-Net in Base 27 — Constructive
(61, 101, 446)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (6, 26, 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
- (35, 75, 370)-net in base 27, using
- 1 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 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, 57, 370)-net over F81, using
- 1 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- digital (6, 26, 76)-net over F27, using
(61, 61+40, 3035)-Net over F27 — Digital
Digital (61, 101, 3035)-net over F27, using
(61, 61+40, 5404046)-Net in Base 27 — Upper bound on s
There is no (61, 101, 5404047)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 696078 600415 968166 503766 970118 873066 191243 571624 195547 548902 824057 989778 397414 192201 655314 650968 874103 353243 947587 517793 616698 639504 707585 363961 > 27101 [i]