MinT - Best Known (62−24, 62, s)-Nets in Base 8

Best Known (62−24, 62, s)-Nets in Base 8

(62−24, 62, 354)-Net over F₈ — Constructive and digital

Digital (38, 62, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 31, 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]

(62−24, 62, 378)-Net over F₈ — Digital

Digital (38, 62, 378)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−24, 62, 35005)-Net in Base 8 — Upper bound on s

There is no (38, 62, 35006)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 089659 217344 933448 546122 793002 630147 849268 094718 207699 > 8⁶² [i]