MinT - Best Known (114−50, 114, s)-Nets in Base 8

Best Known (114−50, 114, s)-Nets in Base 8

(114−50, 114, 354)-Net over F₈ — Constructive and digital

Digital (64, 114, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 57, 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]

(114−50, 114, 19066)-Net in Base 8 — Upper bound on s

There is no (64, 114, 19067)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8 968617 527206 797144 028384 314626 842570 919144 068955 393069 108901 096971 542686 220513 550856 643738 197656 678562 > 8¹¹⁴ [i]