MinT - Best Known (51, 51+41, s)-Nets in Base 8

Best Known (51, 51+41, s)-Nets in Base 8

(51, 51+41, 256)-Net over F₈ — Constructive and digital

Digital (51, 92, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 46, 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]

(51, 51+41, 266)-Net over F₈ — Digital

Digital (51, 92, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 46, 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]

(51, 51+41, 15237)-Net in Base 8 — Upper bound on s

There is no (51, 92, 15238)-net in base 8, because

1 times m-reduction [i] would yield (51, 91, 15238)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15185 695682 540758 754498 321244 529514 237290 482543 582782 527154 082231 554484 312736 133384 > 8⁹¹ [i]