Best Known (102−58, 102, s)-Nets in Base 27
(102−58, 102, 166)-Net over F27 — Constructive and digital
Digital (44, 102, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 36, 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 (8, 66, 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 (7, 36, 82)-net over F27, using
(102−58, 102, 298)-Net over F27 — Digital
Digital (44, 102, 298)-net over F27, using
(102−58, 102, 370)-Net in Base 27 — Constructive
(44, 102, 370)-net in base 27, using
- t-expansion [i] based on (43, 102, 370)-net in base 27, using
- 6 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 6 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(102−58, 102, 48580)-Net in Base 27 — Upper bound on s
There is no (44, 102, 48581)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 99 800583 418483 485933 842409 963889 995956 534626 129807 227528 111751 097579 805566 690070 636270 322671 110889 066689 921683 235610 950846 597002 640657 311424 749395 > 27102 [i]