MinT - Best Known (58, 58+44, s)-Nets in Base 8

Best Known (58, 58+44, s)-Nets in Base 8

(58, 58+44, 354)-Net over F₈ — Constructive and digital

Digital (58, 102, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 51, 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]

(58, 58+44, 19884)-Net in Base 8 — Upper bound on s

There is no (58, 102, 19885)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 468285 043998 943755 303857 293555 209592 221936 631679 324962 477735 698869 119677 706147 294657 198952 > 8¹⁰² [i]