MinT - Best Known (150−52, 150, s)-Nets in Base 3

Best Known (150−52, 150, s)-Nets in Base 3

(150−52, 150, 156)-Net over F₃ — Constructive and digital

Digital (98, 150, 156)-net over F₃, using

2 times m-reduction [i] based on digital (98, 152, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 76, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(150−52, 150, 222)-Net over F₃ — Digital

Digital (98, 150, 222)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−52, 150, 2959)-Net in Base 3 — Upper bound on s

There is no (98, 150, 2960)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 372616 452064 673267 592637 943324 887571 552168 877163 877785 764264 378833 403489 > 3¹⁵⁰ [i]