MinT - Best Known (62, 62+59, s)-Nets in Base 8

Best Known (62, 62+59, s)-Nets in Base 8

(62, 62+59, 160)-Net over F₈ — Constructive and digital

Digital (62, 121, 160)-net over F₈, using

1 times m-reduction [i] based on digital (62, 122, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 61, 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]

(62, 62+59, 226)-Net over F₈ — Digital

Digital (62, 121, 226)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+59, 9079)-Net in Base 8 — Upper bound on s

There is no (62, 121, 9080)-net in base 8, because

1 times m-reduction [i] would yield (62, 120, 9080)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 349193 242460 009434 253048 247077 001788 233358 635164 481747 773478 648574 921959 415617 597015 429326 781892 939047 531844 > 8¹²⁰ [i]