Best Known (31, 31+23, s)-Nets in Base 27
(31, 31+23, 196)-Net over F27 — Constructive and digital
Digital (31, 54, 196)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 11, 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 (4, 15, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (5, 28, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 11, 64)-net over F27, using
(31, 31+23, 370)-Net in Base 27 — Constructive
(31, 54, 370)-net in base 27, using
- 6 times m-reduction [i] based on (31, 60, 370)-net in base 27, using
- base change [i] based on digital (16, 45, 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, 45, 370)-net over F81, using
(31, 31+23, 1147)-Net over F27 — Digital
Digital (31, 54, 1147)-net over F27, using
(31, 31+23, 1488024)-Net in Base 27 — Upper bound on s
There is no (31, 54, 1488025)-net in base 27, because
- 1 times m-reduction [i] would yield (31, 53, 1488025)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 7282 508924 912653 146838 726102 153388 710938 188478 012038 173104 039806 903458 916451 > 2753 [i]