MinT - Best Known (83, 83+32, s)-Nets in Base 3

Best Known (83, 83+32, s)-Nets in Base 3

(83, 83+32, 228)-Net over F₃ — Constructive and digital

Digital (83, 115, 228)-net over F₃, using

3¹ times duplication [i] based on digital (82, 114, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 38, 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]

(83, 83+32, 367)-Net over F₃ — Digital

Digital (83, 115, 367)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+32, 9121)-Net in Base 3 — Upper bound on s

There is no (83, 115, 9122)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 397589 181441 619564 229439 458021 603906 279316 800799 688865 > 3¹¹⁵ [i]