MinT - Best Known (119−57, 119, s)-Nets in Base 8

Best Known (119−57, 119, s)-Nets in Base 8

(119−57, 119, 160)-Net over F₈ — Constructive and digital

Digital (62, 119, 160)-net over F₈, using

3 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]

(119−57, 119, 240)-Net over F₈ — Digital

Digital (62, 119, 240)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−57, 119, 10305)-Net in Base 8 — Upper bound on s

There is no (62, 119, 10306)-net in base 8, because

1 times m-reduction [i] would yield (62, 118, 10306)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36791 583548 252563 332165 672691 107703 509727 740685 636520 368082 261590 800021 128061 034927 964049 658249 279518 674704 > 8¹¹⁸ [i]