MinT - Best Known (109−30, 109, s)-Nets in Base 3

Best Known (109−30, 109, s)-Nets in Base 3

(109−30, 109, 228)-Net over F₃ — Constructive and digital

Digital (79, 109, 228)-net over F₃, using

3¹ times duplication [i] based on digital (78, 108, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 36, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(109−30, 109, 368)-Net over F₃ — Digital

Digital (79, 109, 368)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−30, 109, 9400)-Net in Base 3 — Upper bound on s

There is no (79, 109, 9401)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10153 006683 848453 010917 729531 912847 853113 680716 085067 > 3¹⁰⁹ [i]