Best Known (41, 41+50, s)-Nets in Base 27
(41, 41+50, 170)-Net over F27 — Constructive and digital
Digital (41, 91, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 32, 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 (9, 59, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 32, 82)-net over F27, using
(41, 41+50, 329)-Net over F27 — Digital
Digital (41, 91, 329)-net over F27, using
(41, 41+50, 370)-Net in Base 27 — Constructive
(41, 91, 370)-net in base 27, using
- 9 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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, 75, 370)-net over F81, using
(41, 41+50, 63493)-Net in Base 27 — Upper bound on s
There is no (41, 91, 63494)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 17956 483201 465776 631311 927002 059074 706909 464679 882362 395182 147059 719378 602438 895189 458189 272952 515168 066314 394214 271469 352487 783661 > 2791 [i]