Best Known (18−13, 18, s)-Nets in Base 81
(18−13, 18, 160)-Net over F81 — Constructive and digital
Digital (5, 18, 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
(18−13, 18, 167)-Net over F81 — Digital
Digital (5, 18, 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
(18−13, 18, 9558)-Net in Base 81 — Upper bound on s
There is no (5, 18, 9559)-net in base 81, because
- 1 times m-reduction [i] would yield (5, 17, 9559)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 278 217211 969576 074806 265273 708321 > 8117 [i]