MinT - Best Known (160−42, 160, s)-Nets in Base 3

Best Known (160−42, 160, s)-Nets in Base 3

(160−42, 160, 288)-Net over F₃ — Constructive and digital

Digital (118, 160, 288)-net over F₃, using

3¹ times duplication [i] based on digital (117, 159, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 53, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(160−42, 160, 588)-Net over F₃ — Digital

Digital (118, 160, 588)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−42, 160, 18715)-Net in Base 3 — Upper bound on s

There is no (118, 160, 18716)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21864 484768 762698 917457 247323 181378 149160 539868 303604 882951 744671 932323 803929 > 3¹⁶⁰ [i]