MinT - Best Known (193−58, 193, s)-Nets in Base 3

Best Known (193−58, 193, s)-Nets in Base 3

(193−58, 193, 228)-Net over F₃ — Constructive and digital

Digital (135, 193, 228)-net over F₃, using

3¹ times duplication [i] based on digital (134, 192, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 64, 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]

(193−58, 193, 427)-Net over F₃ — Digital

Digital (135, 193, 427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−58, 193, 8709)-Net in Base 3 — Upper bound on s

There is no (135, 193, 8710)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 603195 773359 063179 619344 885629 729405 893899 799794 872175 407966 390722 023230 898144 529178 967989 > 3¹⁹³ [i]