MinT - Best Known (105−43, 105, s)-Nets in Base 8

Best Known (105−43, 105, s)-Nets in Base 8

(105−43, 105, 354)-Net over F₈ — Constructive and digital

Digital (62, 105, 354)-net over F₈, using

5 times m-reduction [i] based on digital (62, 110, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 55, 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]

(105−43, 105, 429)-Net over F₈ — Digital

Digital (62, 105, 429)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−43, 105, 36786)-Net in Base 8 — Upper bound on s

There is no (62, 105, 36787)-net in base 8, because

1 times m-reduction [i] would yield (62, 104, 36787)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8346 776151 728595 253602 337999 577760 348457 432738 100356 909009 504536 037769 411211 435771 171014 837040 > 8¹⁰⁴ [i]