MinT - Best Known (169−79, 169, s)-Nets in Base 8

Best Known (169−79, 169, s)-Nets in Base 8

(169−79, 169, 256)-Net over F₈ — Constructive and digital

Digital (90, 169, 256)-net over F₈, using

1 times m-reduction [i] based on digital (90, 170, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 85, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(169−79, 169, 357)-Net over F₈ — Digital

Digital (90, 169, 357)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−79, 169, 17058)-Net in Base 8 — Upper bound on s

There is no (90, 169, 17059)-net in base 8, because

1 times m-reduction [i] would yield (90, 168, 17059)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 456080 817659 947645 422231 675160 456698 343226 412777 646340 226655 657688 043468 085975 973881 710466 500915 302236 031150 142109 572953 649664 576710 704108 747784 626816 > 8¹⁶⁸ [i]