MinT - Best Known (91, 91+76, s)-Nets in Base 8

Best Known (91, 91+76, s)-Nets in Base 8

(91, 91+76, 354)-Net over F₈ — Constructive and digital

Digital (91, 167, 354)-net over F₈, using

1 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, 91+76, 397)-Net over F₈ — Digital

Digital (91, 167, 397)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+76, 19953)-Net in Base 8 — Upper bound on s

There is no (91, 167, 19954)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 548097 714113 620695 715103 966595 980809 523663 630415 846480 106891 096357 688525 799292 330990 641272 574983 069440 243851 183626 268123 219339 590924 987895 848722 326360 > 8¹⁶⁷ [i]