MinT - Best Known (48, 48+38, s)-Nets in Base 8

Best Known (48, 48+38, s)-Nets in Base 8

(48, 48+38, 256)-Net over F₈ — Constructive and digital

Digital (48, 86, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 43, 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]

(48, 48+38, 266)-Net over F₈ — Digital

Digital (48, 86, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 43, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(48, 48+38, 13849)-Net in Base 8 — Upper bound on s

There is no (48, 86, 13850)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463754 582652 394184 497378 322434 235001 590045 296633 960289 441500 261373 812153 885236 > 8⁸⁶ [i]