Best Known (39, 39+44, s)-Nets in Base 27
(39, 39+44, 176)-Net over F27 — Constructive and digital
Digital (39, 83, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 29, 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, 54, 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, 29, 82)-net over F27, using
(39, 39+44, 370)-Net in Base 27 — Constructive
(39, 83, 370)-net in base 27, using
- 9 times m-reduction [i] based on (39, 92, 370)-net in base 27, using
- base change [i] based on digital (16, 69, 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, 69, 370)-net over F81, using
(39, 39+44, 378)-Net over F27 — Digital
Digital (39, 83, 378)-net over F27, using
(39, 39+44, 87492)-Net in Base 27 — Upper bound on s
There is no (39, 83, 87493)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 63576 813211 359024 924281 839298 887480 482710 026702 255517 405561 812014 843726 561212 716865 451468 801739 929246 450007 663656 084081 > 2783 [i]