MinT - Best Known (160−88, 160, s)-Nets in Base 8

Best Known (160−88, 160, s)-Nets in Base 8

(160−88, 160, 130)-Net over F₈ — Constructive and digital

Digital (72, 160, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 58, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]
2. digital (14, 102, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(160−88, 160, 176)-Net over F₈ — Digital

Digital (72, 160, 176)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−88, 160, 4712)-Net in Base 8 — Upper bound on s

There is no (72, 160, 4713)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 139997 910523 341567 425102 394334 639202 044668 636659 142710 206508 079739 029317 867567 845599 577263 420022 958071 604688 872529 690705 475827 984188 720965 240176 > 8¹⁶⁰ [i]