MinT - Best Known (111−50, 111, s)-Nets in Base 8

Best Known (111−50, 111, s)-Nets in Base 8

(111−50, 111, 256)-Net over F₈ — Constructive and digital

Digital (61, 111, 256)-net over F₈, using

1 times m-reduction [i] based on digital (61, 112, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 56, 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]

(111−50, 111, 292)-Net over F₈ — Digital

Digital (61, 111, 292)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−50, 111, 14852)-Net in Base 8 — Upper bound on s

There is no (61, 111, 14853)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17519 944626 822351 028359 604293 133556 423421 328620 818046 413876 899211 582596 905954 840908 406980 463961 374976 > 8¹¹¹ [i]