Best Known (82−61, 82, s)-Nets in Base 9
(82−61, 82, 74)-Net over F9 — Constructive and digital
Digital (21, 82, 74)-net over F9, using
- t-expansion [i] based on digital (17, 82, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
(82−61, 82, 88)-Net over F9 — Digital
Digital (21, 82, 88)-net over F9, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
(82−61, 82, 549)-Net in Base 9 — Upper bound on s
There is no (21, 82, 550)-net in base 9, because
- 1 times m-reduction [i] would yield (21, 81, 550)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 200120 149281 101313 596319 248830 861754 831064 263838 986416 869769 547152 132812 942177 > 981 [i]