Best Known (61, 61+42, s)-Nets in Base 27
(61, 61+42, 264)-Net over F27 — Constructive and digital
Digital (61, 103, 264)-net over F27, using
- 1 times m-reduction [i] based on digital (61, 104, 264)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 21, 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 (9, 30, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 53, 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, 21, 82)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(61, 61+42, 434)-Net in Base 27 — Constructive
(61, 103, 434)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 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
- (36, 78, 370)-net in base 27, using
- 2 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- base change [i] based on digital (16, 60, 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, 60, 370)-net over F81, using
- 2 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- digital (4, 25, 64)-net over F27, using
(61, 61+42, 2468)-Net over F27 — Digital
Digital (61, 103, 2468)-net over F27, using
(61, 61+42, 3499583)-Net in Base 27 — Upper bound on s
There is no (61, 103, 3499584)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 445659 168905 348385 776661 908871 731960 555695 229662 158034 684796 523446 655899 397143 939207 840631 782090 585461 441774 647046 531820 683234 455687 125181 037185 > 27103 [i]