MinT - Best Known (91, 165, s)-Nets in Base 8

Best Known (91, 165, s)-Nets in Base 8

(91, 165, 354)-Net over F₈ — Constructive and digital

Digital (91, 165, 354)-net over F₈, using

3 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(91, 165, 417)-Net over F₈ — Digital

Digital (91, 165, 417)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 165, 22266)-Net in Base 8 — Upper bound on s

There is no (91, 165, 22267)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102367 890531 660176 661079 272360 684228 583577 952679 111699 675077 749448 646401 302985 736751 401786 109085 944635 792337 679092 255322 986192 745638 835699 846958 580636 > 8¹⁶⁵ [i]