MinT - Best Known (48, 82, s)-Nets in Base 8

Best Known (48, 82, s)-Nets in Base 8

(48, 82, 354)-Net over F₈ — Constructive and digital

Digital (48, 82, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 41, 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]

(48, 82, 23266)-Net in Base 8 — Upper bound on s

There is no (48, 82, 23267)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 107849 232019 806519 256012 462446 833559 799319 847190 916360 702142 082416 600060 > 8⁸² [i]