MinT - Best Known (108−53, 108, s)-Nets in Base 8

Best Known (108−53, 108, s)-Nets in Base 8

(108−53, 108, 160)-Net over F₈ — Constructive and digital

Digital (55, 108, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 54, 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]

(108−53, 108, 201)-Net over F₈ — Digital

Digital (55, 108, 201)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−53, 108, 7831)-Net in Base 8 — Upper bound on s

There is no (55, 108, 7832)-net in base 8, because

1 times m-reduction [i] would yield (55, 107, 7832)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 275208 554719 376687 925834 519510 577148 908713 382487 694390 904240 767306 922198 175387 282885 009111 700400 > 8¹⁰⁷ [i]