Best Known (5, 5+43, s)-Nets in Base 81
(5, 5+43, 160)-Net over F81 — Constructive and digital
Digital (5, 48, 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+43, 167)-Net over F81 — Digital
Digital (5, 48, 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+43, 2016)-Net in Base 81 — Upper bound on s
There is no (5, 48, 2017)-net in base 81, because
- 1 times m-reduction [i] would yield (5, 47, 2017)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 503047 479267 641767 447332 342156 202620 662962 028603 423525 976466 677568 750226 722073 076456 060561 > 8147 [i]