MinT - Best Known (50−25, 50, s)-Nets in Base 9

Best Known (50−25, 50, s)-Nets in Base 9

(50−25, 50, 164)-Net over F₉ — Constructive and digital

Digital (25, 50, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 25, 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]

(50−25, 50, 5202)-Net in Base 9 — Upper bound on s

There is no (25, 50, 5203)-net in base 9, because

1 times m-reduction [i] would yield (25, 49, 5203)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 57384 240094 561679 240569 848313 285184 524279 549473 > 9⁴⁹ [i]