MinT - Best Known (89, 89+63, s)-Nets in Base 8

Best Known (89, 89+63, s)-Nets in Base 8

(89, 89+63, 354)-Net over F₈ — Constructive and digital

Digital (89, 152, 354)-net over F₈, using

12 times m-reduction [i] based on digital (89, 164, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 82, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(89, 89+63, 548)-Net over F₈ — Digital

Digital (89, 152, 548)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+63, 44429)-Net in Base 8 — Upper bound on s

There is no (89, 152, 44430)-net in base 8, because

1 times m-reduction [i] would yield (89, 151, 44430)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23273 855284 877142 702482 918578 144981 857339 720664 415616 954044 201171 015311 192912 204405 336162 110442 831433 971206 651543 265119 428696 666055 529536 > 8¹⁵¹ [i]