MinT - Best Known (160−44, 160, s)-Nets in Base 3

Best Known (160−44, 160, s)-Nets in Base 3

(160−44, 160, 264)-Net over F₃ — Constructive and digital

Digital (116, 160, 264)-net over F₃, using

3¹ times duplication [i] based on digital (115, 159, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 53, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(160−44, 160, 494)-Net over F₃ — Digital

Digital (116, 160, 494)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−44, 160, 13338)-Net in Base 3 — Upper bound on s

There is no (116, 160, 13339)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21876 740791 357679 232505 754080 790981 204709 925358 955478 723530 232218 748715 320173 > 3¹⁶⁰ [i]