MinT - Best Known (103−41, 103, s)-Nets in Base 8

Best Known (103−41, 103, s)-Nets in Base 8

(103−41, 103, 354)-Net over F₈ — Constructive and digital

Digital (62, 103, 354)-net over F₈, using

7 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]

(103−41, 103, 486)-Net over F₈ — Digital

Digital (62, 103, 486)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−41, 103, 47847)-Net in Base 8 — Upper bound on s

There is no (62, 103, 47848)-net in base 8, because

1 times m-reduction [i] would yield (62, 102, 47848)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 423155 742225 214760 434117 977123 122927 754761 744514 011972 107202 123011 809039 032984 616997 937766 > 8¹⁰² [i]