MinT - Best Known (91, 91+55, s)-Nets in Base 8

Best Known (91, 91+55, s)-Nets in Base 8

(91, 91+55, 354)-Net over F₈ — Constructive and digital

Digital (91, 146, 354)-net over F₈, using

22 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+55, 432)-Net in Base 8 — Constructive

(91, 146, 432)-net in base 8, using

4 times m-reduction [i] based on (91, 150, 432)-net in base 8, using
- trace code for nets [i] based on (16, 75, 216)-net in base 64, using
  - 2 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
    - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(91, 91+55, 841)-Net over F₈ — Digital

Digital (91, 146, 841)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+55, 110451)-Net in Base 8 — Upper bound on s

There is no (91, 146, 110452)-net in base 8, because

1 times m-reduction [i] would yield (91, 145, 110452)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88744 296927 058395 832580 813778 929936 726315 287044 419378 703674 478911 740854 210739 168201 635648 262151 471693 509935 385473 796684 204663 468044 > 8¹⁴⁵ [i]