Best Known (37, 37+42, s)-Nets in Base 27
(37, 37+42, 170)-Net over F27 — Constructive and digital
Digital (37, 79, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 28, 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, 51, 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 (7, 28, 82)-net over F27, using
(37, 37+42, 358)-Net over F27 — Digital
Digital (37, 79, 358)-net over F27, using
(37, 37+42, 370)-Net in Base 27 — Constructive
(37, 79, 370)-net in base 27, using
- 5 times m-reduction [i] based on (37, 84, 370)-net in base 27, using
- base change [i] based on digital (16, 63, 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, 63, 370)-net over F81, using
(37, 37+42, 80931)-Net in Base 27 — Upper bound on s
There is no (37, 79, 80932)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 119629 949758 724194 481089 686649 747142 959790 628202 212082 887080 089671 513987 544646 131602 324293 339384 944958 705463 523209 > 2779 [i]