MinT - Best Known (84−41, 84, s)-Nets in Base 8

Best Known (84−41, 84, s)-Nets in Base 8

(84−41, 84, 160)-Net over F₈ — Constructive and digital

Digital (43, 84, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 42, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(84−41, 84, 168)-Net over F₈ — Digital

Digital (43, 84, 168)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−41, 84, 6625)-Net in Base 8 — Upper bound on s

There is no (43, 84, 6626)-net in base 8, because

1 times m-reduction [i] would yield (43, 83, 6626)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 905 814093 026569 978533 816990 159460 211882 238292 002651 650828 290345 592897 261176 > 8⁸³ [i]