Best Known (72−28, 72, s)-Nets in Base 27
(72−28, 72, 246)-Net over F27 — Constructive and digital
Digital (44, 72, 246)-net over F27, using
- 1 times m-reduction [i] based on digital (44, 73, 246)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 16, 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, 21, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 36, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 16, 82)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(72−28, 72, 370)-Net in Base 27 — Constructive
(44, 72, 370)-net in base 27, using
- t-expansion [i] based on (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
- 36 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(72−28, 72, 2770)-Net over F27 — Digital
Digital (44, 72, 2770)-net over F27, using
(72−28, 72, 5342975)-Net in Base 27 — Upper bound on s
There is no (44, 72, 5342976)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 11 433828 044513 924999 575701 765566 035263 662899 391784 990967 961459 522821 988966 078915 833051 890941 676232 432129 > 2772 [i]