MinT - Best Known (159−73, 159, s)-Nets in Base 8

Best Known (159−73, 159, s)-Nets in Base 8

(159−73, 159, 256)-Net over F₈ — Constructive and digital

Digital (86, 159, 256)-net over F₈, using

3 times m-reduction [i] based on digital (86, 162, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 81, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(159−73, 159, 367)-Net over F₈ — Digital

Digital (86, 159, 367)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−73, 159, 18735)-Net in Base 8 — Upper bound on s

There is no (86, 159, 18736)-net in base 8, because

1 times m-reduction [i] would yield (86, 158, 18736)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48779 603741 803723 162318 746956 197433 496817 739447 755179 563370 461467 513132 757649 296345 486094 944750 029821 643002 060495 961427 180550 308700 084796 697801 > 8¹⁵⁸ [i]