Best Known (37, 77, s)-Nets in Base 27
(37, 77, 176)-Net over F27 — Constructive and digital
Digital (37, 77, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 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 (10, 50, 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, 27, 82)-net over F27, using
(37, 77, 370)-Net in Base 27 — Constructive
(37, 77, 370)-net in base 27, using
- 7 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, 77, 405)-Net over F27 — Digital
Digital (37, 77, 405)-net over F27, using
(37, 77, 103523)-Net in Base 27 — Upper bound on s
There is no (37, 77, 103524)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 164 068335 746498 123210 333719 025673 380241 741470 399476 928829 213494 604965 943584 906707 727698 671323 379352 396558 875201 > 2777 [i]