MinT - Best Known (68, 68+66, s)-Nets in Base 8

Best Known (68, 68+66, s)-Nets in Base 8

(68, 68+66, 160)-Net over F₈ — Constructive and digital

Digital (68, 134, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 67, 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]

(68, 68+66, 236)-Net over F₈ — Digital

Digital (68, 134, 236)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+66, 8716)-Net in Base 8 — Upper bound on s

There is no (68, 134, 8717)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 367013 731626 816716 209438 494646 110685 039038 217437 066859 614791 515488 758641 686291 258543 226739 470552 658728 859900 061412 187456 > 8¹³⁴ [i]