MinT - Best Known (150, 150+91, s)-Nets in Base 3

Best Known (150, 150+91, s)-Nets in Base 3

(150, 150+91, 156)-Net over F₃ — Constructive and digital

Digital (150, 241, 156)-net over F₃, using

t-expansion [i] based on digital (147, 241, 156)-net over F₃, using
- 9 times m-reduction [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+91, 259)-Net over F₃ — Digital

Digital (150, 241, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+91, 3044)-Net in Base 3 — Upper bound on s

There is no (150, 241, 3045)-net in base 3, because

1 times m-reduction [i] would yield (150, 240, 3045)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 249583 408121 986778 344162 188607 165079 285593 705767 737695 131701 864814 311287 625388 464680 281262 591332 078330 607557 098555 > 3²⁴⁰ [i]