MinT - Best Known (58, 58+47, s)-Nets in Base 8

Best Known (58, 58+47, s)-Nets in Base 8

(58, 58+47, 256)-Net over F₈ — Constructive and digital

Digital (58, 105, 256)-net over F₈, using

1 times m-reduction [i] based on digital (58, 106, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 53, 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]

(58, 58+47, 287)-Net over F₈ — Digital

Digital (58, 105, 287)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+47, 16312)-Net in Base 8 — Upper bound on s

There is no (58, 105, 16313)-net in base 8, because

1 times m-reduction [i] would yield (58, 104, 16313)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8351 797406 055930 460328 730436 904587 596230 791801 627347 499588 539227 807973 627827 059333 387926 067224 > 8¹⁰⁴ [i]