MinT - Best Known (90, 166, s)-Nets in Base 8

Best Known (90, 166, s)-Nets in Base 8

(90, 166, 354)-Net over F₈ — Constructive and digital

Digital (90, 166, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 83, 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]

(90, 166, 385)-Net over F₈ — Digital

Digital (90, 166, 385)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 166, 18890)-Net in Base 8 — Upper bound on s

There is no (90, 166, 18891)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 819928 156168 299770 895797 415200 943113 449491 924242 932711 457675 030519 387499 827379 158872 687533 271045 671938 167166 586890 505246 337436 620059 532097 368667 119092 > 8¹⁶⁶ [i]