MinT - Best Known (101, 101+71, s)-Nets in Base 8

Best Known (101, 101+71, s)-Nets in Base 8

(101, 101+71, 354)-Net over F₈ — Constructive and digital

Digital (101, 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]

(101, 101+71, 620)-Net over F₈ — Digital

Digital (101, 172, 620)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+71, 51312)-Net in Base 8 — Upper bound on s

There is no (101, 172, 51313)-net in base 8, because

1 times m-reduction [i] would yield (101, 171, 51313)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26833 215612 664371 275345 930204 539829 593391 766647 862425 660288 564341 451860 833707 484174 783535 727020 380980 502408 879805 031546 078219 121203 764805 603538 283055 106384 > 8¹⁷¹ [i]