MinT - Best Known (209−50, 209, s)-Nets in Base 3

Best Known (209−50, 209, s)-Nets in Base 3

(209−50, 209, 464)-Net over F₃ — Constructive and digital

Digital (159, 209, 464)-net over F₃, using

3¹ times duplication [i] based on digital (158, 208, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 52, 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]

(209−50, 209, 1052)-Net over F₃ — Digital

Digital (159, 209, 1052)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−50, 209, 49558)-Net in Base 3 — Upper bound on s

There is no (159, 209, 49559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5230 372163 613307 173989 791183 048361 786702 011569 684960 802816 703286 278498 089081 051052 990539 967144 059647 > 3²⁰⁹ [i]