MinT - Best Known (150−62, 150, s)-Nets in Base 3

Best Known (150−62, 150, s)-Nets in Base 3

(150−62, 150, 128)-Net over F₃ — Constructive and digital

Digital (88, 150, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 75, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(150−62, 150, 133)-Net over F₃ — Digital

Digital (88, 150, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−62, 150, 1233)-Net in Base 3 — Upper bound on s

There is no (88, 150, 1234)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 374249 659702 435646 076799 340531 239149 830442 186766 530466 640622 724764 567225 > 3¹⁵⁰ [i]