MinT - Best Known (66−33, 66, s)-Nets in Base 9

Best Known (66−33, 66, s)-Nets in Base 9

(66−33, 66, 164)-Net over F₉ — Constructive and digital

Digital (33, 66, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 33, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(66−33, 66, 6388)-Net in Base 9 — Upper bound on s

There is no (33, 66, 6389)-net in base 9, because

1 times m-reduction [i] would yield (33, 65, 6389)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106 185770 276379 289958 344649 152452 929486 781076 121317 956991 814785 > 9⁶⁵ [i]