Best Known (82−47, 82, s)-Nets in Base 81
(82−47, 82, 370)-Net over F81 — Constructive and digital
Digital (35, 82, 370)-net over F81, using
- t-expansion [i] based on digital (16, 82, 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
(82−47, 82, 612)-Net over F81 — Digital
Digital (35, 82, 612)-net over F81, using
- net from sequence [i] based on digital (35, 611)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 35 and N(F) ≥ 612, using
(82−47, 82, 620218)-Net in Base 81 — Upper bound on s
There is no (35, 82, 620219)-net in base 81, because
- 1 times m-reduction [i] would yield (35, 81, 620219)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 38662 825185 541137 246381 769334 742676 791999 659483 351943 958140 083570 089197 495610 109567 385723 956297 371500 344716 943615 868613 832340 523070 023555 229641 064022 290961 > 8181 [i]