MinT - Best Known (130−53, 130, s)-Nets in Base 8

Best Known (130−53, 130, s)-Nets in Base 8

(130−53, 130, 354)-Net over F₈ — Constructive and digital

Digital (77, 130, 354)-net over F₈, using

10 times m-reduction [i] based on digital (77, 140, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 70, 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]

(130−53, 130, 519)-Net over F₈ — Digital

Digital (77, 130, 519)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−53, 130, 45578)-Net in Base 8 — Upper bound on s

There is no (77, 130, 45579)-net in base 8, because

1 times m-reduction [i] would yield (77, 129, 45579)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 315 377249 916736 649515 209727 713365 009754 136493 435098 509112 283204 970169 899554 423733 843706 977407 903126 866397 628390 800416 > 8¹²⁹ [i]