Best Known (46, 109, s)-Nets in Base 27
(46, 109, 166)-Net over F27 — Constructive and digital
Digital (46, 109, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 38, 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, 71, 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, 38, 82)-net over F27, using
(46, 109, 288)-Net over F27 — Digital
Digital (46, 109, 288)-net over F27, using
(46, 109, 370)-Net in Base 27 — Constructive
(46, 109, 370)-net in base 27, using
- 271 times duplication [i] based on (45, 108, 370)-net in base 27, using
- t-expansion [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
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
(46, 109, 46301)-Net in Base 27 — Upper bound on s
There is no (46, 109, 46302)-net in base 27, because
- 1 times m-reduction [i] would yield (46, 108, 46302)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 38676 868016 988337 021465 437811 084850 856653 787609 939582 340778 232828 283900 298393 728788 779235 063730 818063 121115 764175 384314 323194 485214 014952 055616 140470 632729 > 27108 [i]