MinT - Best Known (62, 62+45, s)-Nets in Base 8

Best Known (62, 62+45, s)-Nets in Base 8

(62, 62+45, 354)-Net over F₈ — Constructive and digital

Digital (62, 107, 354)-net over F₈, using

3 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]

(62, 62+45, 384)-Net over F₈ — Digital

Digital (62, 107, 384)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+45, 29027)-Net in Base 8 — Upper bound on s

There is no (62, 107, 29028)-net in base 8, because

1 times m-reduction [i] would yield (62, 106, 29028)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534386 650050 638712 761964 844111 025407 559008 432454 485390 250073 182272 671859 277973 944867 367971 107832 > 8¹⁰⁶ [i]