MinT - Best Known (112−51, 112, s)-Nets in Base 8

Best Known (112−51, 112, s)-Nets in Base 8

(112−51, 112, 256)-Net over F₈ — Constructive and digital

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]

(112−51, 112, 281)-Net over F₈ — Digital

Digital (61, 112, 281)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−51, 112, 14852)-Net in Base 8 — Upper bound on s

There is no (61, 112, 14853)-net in base 8, because

1 times m-reduction [i] would yield (61, 111, 14853)-net in base 8, but
- 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]