MinT - Best Known (155, 155+46, s)-Nets in Base 3

Best Known (155, 155+46, s)-Nets in Base 3

(155, 155+46, 600)-Net over F₃ — Constructive and digital

Digital (155, 201, 600)-net over F₃, using

3¹ times duplication [i] based on digital (154, 200, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 50, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(155, 155+46, 1214)-Net over F₃ — Digital

Digital (155, 201, 1214)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+46, 69648)-Net in Base 3 — Upper bound on s

There is no (155, 201, 69649)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797009 935127 429205 013889 388620 705631 487072 217012 586578 605011 823197 659576 816218 259329 961222 690955 > 3²⁰¹ [i]