MinT - Best Known (138−62, 138, s)-Nets in Base 8

Best Known (138−62, 138, s)-Nets in Base 8

(138−62, 138, 354)-Net over F₈ — Constructive and digital

Digital (76, 138, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 69, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(138−62, 138, 18564)-Net in Base 8 — Upper bound on s

There is no (76, 138, 18565)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42329 050768 008983 060397 748922 852760 270929 330579 387289 604087 686617 119551 895211 800309 636627 374248 374704 621829 120778 704148 765824 > 8¹³⁸ [i]