MinT - Best Known (160−70, 160, s)-Nets in Base 8

Best Known (160−70, 160, s)-Nets in Base 8

(160−70, 160, 354)-Net over F₈ — Constructive and digital

Digital (90, 160, 354)-net over F₈, using

6 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(160−70, 160, 451)-Net over F₈ — Digital

Digital (90, 160, 451)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−70, 160, 26682)-Net in Base 8 — Upper bound on s

There is no (90, 160, 26683)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 125618 555070 807982 922992 867621 737721 299410 803202 641093 474027 890182 631200 303033 390333 917777 952206 557488 675812 560652 389736 259916 375979 794094 283952 > 8¹⁶⁰ [i]