Best Known (45, 106, s)-Nets in Base 27
(45, 106, 166)-Net over F27 — Constructive and digital
Digital (45, 106, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 37, 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, 69, 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, 37, 82)-net over F27, using
(45, 106, 288)-Net over F27 — Digital
Digital (45, 106, 288)-net over F27, using
(45, 106, 370)-Net in Base 27 — Constructive
(45, 106, 370)-net in base 27, using
- t-expansion [i] based on (43, 106, 370)-net in base 27, using
- 2 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
- 2 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(45, 106, 47363)-Net in Base 27 — Upper bound on s
There is no (45, 106, 47364)-net in base 27, because
- 1 times m-reduction [i] would yield (45, 105, 47364)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 964701 378143 693646 929430 313029 899433 496098 795963 526077 237146 018667 526209 987688 280525 024309 871776 606310 337850 385260 185832 943382 724379 580627 282060 983769 > 27105 [i]