MinT - Best Known (157−40, 157, s)-Nets in Base 3

Best Known (157−40, 157, s)-Nets in Base 3

(157−40, 157, 288)-Net over F₃ — Constructive and digital

Digital (117, 157, 288)-net over F₃, using

2 times m-reduction [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]

(157−40, 157, 651)-Net over F₃ — Digital

Digital (117, 157, 651)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−40, 157, 23084)-Net in Base 3 — Upper bound on s

There is no (117, 157, 23085)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 849275 339735 637233 137891 694079 154055 474790 340106 250974 793864 035151 439697 > 3¹⁵⁷ [i]