MinT - Best Known (145−65, 145, s)-Nets in Base 8

Best Known (145−65, 145, s)-Nets in Base 8

(145−65, 145, 354)-Net over F₈ — Constructive and digital

Digital (80, 145, 354)-net over F₈, using

1 times m-reduction [i] based on digital (80, 146, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 73, 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]

(145−65, 145, 373)-Net over F₈ — Digital

Digital (80, 145, 373)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−65, 145, 21148)-Net in Base 8 — Upper bound on s

There is no (80, 145, 21149)-net in base 8, because

1 times m-reduction [i] would yield (80, 144, 21149)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11102 468960 311968 261435 818358 521702 227710 358577 121333 068568 107750 773351 507560 375006 394963 480589 888353 881418 055898 168030 518105 302516 > 8¹⁴⁴ [i]