Best Known (69−43, 69, s)-Nets in Base 81
(69−43, 69, 370)-Net over F81 — Constructive and digital
Digital (26, 69, 370)-net over F81, using
- t-expansion [i] based on digital (16, 69, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(69−43, 69, 500)-Net over F81 — Digital
Digital (26, 69, 500)-net over F81, using
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
(69−43, 69, 164146)-Net in Base 81 — Upper bound on s
There is no (26, 69, 164147)-net in base 81, because
- 1 times m-reduction [i] would yield (26, 68, 164147)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5984 225253 141312 849695 105090 730830 054464 366292 226084 774667 155613 373072 501779 331277 331113 981478 466241 939078 657653 539241 876614 838961 > 8168 [i]