MinT - Best Known (56, 98, s)-Nets in Base 8

Best Known (56, 98, s)-Nets in Base 8

(56, 98, 354)-Net over F₈ — Constructive and digital

Digital (56, 98, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 49, 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]

(56, 98, 20301)-Net in Base 8 — Upper bound on s

There is no (56, 98, 20302)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31832 234543 499871 207450 467456 445356 906860 087686 652000 925124 410003 485701 358308 044653 236180 > 8⁹⁸ [i]