MinT - Best Known (46−23, 46, s)-Nets in Base 9

Best Known (46−23, 46, s)-Nets in Base 9

(46−23, 46, 164)-Net over F₉ — Constructive and digital

Digital (23, 46, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 23, 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]

(46−23, 46, 4909)-Net in Base 9 — Upper bound on s

There is no (23, 46, 4910)-net in base 9, because

1 times m-reduction [i] would yield (23, 45, 4910)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 728239 220408 328198 319012 573722 816736 454545 > 9⁴⁵ [i]