Best Known (5, 5+44, s)-Nets in Base 81
(5, 5+44, 160)-Net over F81 — Constructive and digital
Digital (5, 49, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
(5, 5+44, 167)-Net over F81 — Digital
Digital (5, 49, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
(5, 5+44, 2005)-Net in Base 81 — Upper bound on s
There is no (5, 49, 2006)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3308 437110 362302 893257 941444 621601 931164 411469 031641 630684 583575 229626 830457 515580 099197 456961 > 8149 [i]