Best Known (72−29, 72, s)-Nets in Base 27
(72−29, 72, 240)-Net over F27 — Constructive and digital
Digital (43, 72, 240)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 15, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 21, 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 (7, 36, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (6, 15, 76)-net over F27, using
(72−29, 72, 370)-Net in Base 27 — Constructive
(43, 72, 370)-net in base 27, using
- 36 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
(72−29, 72, 2097)-Net over F27 — Digital
Digital (43, 72, 2097)-net over F27, using
(72−29, 72, 4222238)-Net in Base 27 — Upper bound on s
There is no (43, 72, 4222239)-net in base 27, because
- 1 times m-reduction [i] would yield (43, 71, 4222239)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 423475 252833 680435 430015 519078 560811 796140 485944 404966 246297 963778 640228 552590 444689 302273 779381 402581 > 2771 [i]