MinT - Best Known (66, 66+49, s)-Nets in Base 8

Best Known (66, 66+49, s)-Nets in Base 8

(66, 66+49, 354)-Net over F₈ — Constructive and digital

Digital (66, 115, 354)-net over F₈, using

3 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 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]

(66, 66+49, 384)-Net over F₈ — Digital

Digital (66, 115, 384)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+49, 27271)-Net in Base 8 — Upper bound on s

There is no (66, 115, 27272)-net in base 8, because

1 times m-reduction [i] would yield (66, 114, 27272)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8 965159 515468 784434 426234 734120 608626 239165 744336 983131 606107 980367 963187 835023 368566 819852 401286 130992 > 8¹¹⁴ [i]