MinT - Best Known (142−68, 142, s)-Nets in Base 8

Best Known (142−68, 142, s)-Nets in Base 8

(142−68, 142, 208)-Net over F₈ — Constructive and digital

Digital (74, 142, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 71, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(142−68, 142, 278)-Net over F₈ — Digital

Digital (74, 142, 278)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−68, 142, 11410)-Net in Base 8 — Upper bound on s

There is no (74, 142, 11411)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 687919 444718 236719 438349 550686 079653 392324 755304 422471 887197 189938 879349 265293 800093 391830 017906 575959 020044 574118 120190 799540 > 8¹⁴² [i]