MinT - Best Known (77, 77+74, s)-Nets in Base 8

Best Known (77, 77+74, s)-Nets in Base 8

(77, 77+74, 160)-Net over F₈ — Constructive and digital

Digital (77, 151, 160)-net over F₈, using

1 times m-reduction [i] based on digital (77, 152, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 76, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(77, 77+74, 266)-Net over F₈ — Digital

Digital (77, 151, 266)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+74, 10125)-Net in Base 8 — Upper bound on s

There is no (77, 151, 10126)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23333 370961 372357 596496 930026 020294 995506 613921 125374 733073 875951 030834 889278 099386 391282 397466 937027 967051 519068 593039 802223 170971 340308 > 8¹⁵¹ [i]