Best Known (6, 6+23, s)-Nets in Base 81
(6, 6+23, 160)-Net over F81 — Constructive and digital
Digital (6, 29, 160)-net over F81, using
- t-expansion [i] based on digital (5, 29, 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
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(6, 6+23, 190)-Net over F81 — Digital
Digital (6, 29, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(6, 6+23, 4419)-Net in Base 81 — Upper bound on s
There is no (6, 29, 4420)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 28, 4420)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 274174 599478 850954 297262 778171 629632 247197 264109 809601 > 8128 [i]