MinT - Best Known (46, 81, s)-Nets in Base 8

Best Known (46, 81, s)-Nets in Base 8

(46, 81, 256)-Net over F₈ — Constructive and digital

Digital (46, 81, 256)-net over F₈, using

1 times m-reduction [i] based on digital (46, 82, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 41, 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]

(46, 81, 275)-Net over F₈ — Digital

Digital (46, 81, 275)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 81, 18215)-Net in Base 8 — Upper bound on s

There is no (46, 81, 18216)-net in base 8, because

1 times m-reduction [i] would yield (46, 80, 18216)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 768170 864656 682086 220157 066127 037142 810491 931801 264546 269104 892338 097630 > 8⁸⁰ [i]