MinT - Best Known (172−77, 172, s)-Nets in Base 8

Best Known (172−77, 172, s)-Nets in Base 8

(172−77, 172, 354)-Net over F₈ — Constructive and digital

Digital (95, 172, 354)-net over F₈, using

t-expansion [i] based on digital (93, 172, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 86, 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]

(172−77, 172, 436)-Net over F₈ — Digital

Digital (95, 172, 436)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−77, 172, 24842)-Net in Base 8 — Upper bound on s

There is no (95, 172, 24843)-net in base 8, because

1 times m-reduction [i] would yield (95, 171, 24843)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26843 674628 402671 243294 642368 960706 522387 897143 277201 917842 422876 042178 330665 747822 282650 162338 107546 487062 897092 880398 070962 523125 072877 185042 132969 035888 > 8¹⁷¹ [i]