MinT - Best Known (190, 190+60, s)-Nets in Base 3

Best Known (190, 190+60, s)-Nets in Base 3

(190, 190+60, 464)-Net over F₃ — Constructive and digital

Digital (190, 250, 464)-net over F₃, using

3² times duplication [i] based on digital (188, 248, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 62, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(190, 190+60, 1204)-Net over F₃ — Digital

Digital (190, 250, 1204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190, 190+60, 56956)-Net in Base 3 — Upper bound on s

There is no (190, 250, 56957)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190720 714178 841301 208564 693002 054402 934381 898275 648340 961948 841534 815265 420136 472077 509216 336897 458946 031633 900286 172625 > 3²⁵⁰ [i]