MinT - Best Known (110−48, 110, s)-Nets in Base 8

Best Known (110−48, 110, s)-Nets in Base 8

(110−48, 110, 354)-Net over F₈ — Constructive and digital

Digital (62, 110, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 55, 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]

(110−48, 110, 19279)-Net in Base 8 — Upper bound on s

There is no (62, 110, 19280)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2189 180458 466982 518189 004359 908708 380087 541945 700148 700068 094442 747723 281358 670499 625171 703498 353356 > 8¹¹⁰ [i]