MinT - Best Known (77, 77+53, s)-Nets in Base 9

Best Known (77, 77+53, s)-Nets in Base 9

(77, 77+53, 344)-Net over F₉ — Constructive and digital

Digital (77, 130, 344)-net over F₉, using

10 times m-reduction [i] based on digital (77, 140, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 70, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(77, 77+53, 617)-Net over F₉ — Digital

Digital (77, 130, 617)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+53, 71551)-Net in Base 9 — Upper bound on s

There is no (77, 130, 71552)-net in base 9, because

1 times m-reduction [i] would yield (77, 129, 71552)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 330210 999959 664869 396939 673546 424669 738763 374133 957564 079371 696779 391401 830207 754297 450809 130424 120274 576712 425871 099905 > 9¹²⁹ [i]