MinT - Best Known (75−57, 75, s)-Nets in Base 9

Best Known (75−57, 75, s)-Nets in Base 9

(75−57, 75, 74)-Net over F₉ — Constructive and digital

Digital (18, 75, 74)-net over F₉, using

t-expansion [i] based on digital (17, 75, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(75−57, 75, 452)-Net in Base 9 — Upper bound on s

There is no (18, 75, 453)-net in base 9, because

1 times m-reduction [i] would yield (18, 74, 453)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41348 468581 281932 619494 954748 567580 609884 808722 811674 791563 735719 906785 > 9⁷⁴ [i]