MinT - Best Known (83, 83+73, s)-Nets in Base 8

Best Known (83, 83+73, s)-Nets in Base 8

(83, 83+73, 256)-Net over F₈ — Constructive and digital

Digital (83, 156, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 78, 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]

(83, 83+73, 332)-Net over F₈ — Digital

Digital (83, 156, 332)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+73, 15751)-Net in Base 8 — Upper bound on s

There is no (83, 156, 15752)-net in base 8, because

1 times m-reduction [i] would yield (83, 155, 15752)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 395463 251514 640861 888439 852387 785819 308717 819811 905888 411497 198591 329747 271878 885183 054836 050061 298175 505980 305763 928511 668896 465548 044220 > 8¹⁵⁵ [i]