Best Known (82−70, 82, s)-Nets in Base 27
(82−70, 82, 96)-Net over F27 — Constructive and digital
Digital (12, 82, 96)-net over F27, using
- t-expansion [i] based on digital (11, 82, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(82−70, 82, 109)-Net over F27 — Digital
Digital (12, 82, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(82−70, 82, 1188)-Net in Base 27 — Upper bound on s
There is no (12, 82, 1189)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2361 404284 015070 336992 956009 670952 433009 793596 648778 803776 536871 916321 182040 233612 802642 000376 482701 139929 803665 912147 > 2782 [i]