MinT - Best Known (150, 150+100, s)-Nets in Base 3

Best Known (150, 150+100, s)-Nets in Base 3

(150, 150+100, 156)-Net over F₃ — Constructive and digital

Digital (150, 250, 156)-net over F₃, using

t-expansion [i] based on digital (147, 250, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 125, 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, 150+100, 227)-Net over F₃ — Digital

Digital (150, 250, 227)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+100, 2318)-Net in Base 3 — Upper bound on s

There is no (150, 250, 2319)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194169 486090 014784 359353 509770 971471 150583 214936 482131 122081 946602 049180 361088 718005 555534 798371 181446 817575 983501 481917 > 3²⁵⁰ [i]