MinT - Best Known (247−101, 247, s)-Nets in Base 3

Best Known (247−101, 247, s)-Nets in Base 3

(247−101, 247, 156)-Net over F₃ — Constructive and digital

Digital (146, 247, 156)-net over F₃, using

1 times m-reduction [i] based on digital (146, 248, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 124, 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]

(247−101, 247, 211)-Net over F₃ — Digital

Digital (146, 247, 211)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−101, 247, 2119)-Net in Base 3 — Upper bound on s

There is no (146, 247, 2120)-net in base 3, because

1 times m-reduction [i] would yield (146, 246, 2120)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2408 508608 579359 781307 864418 673568 578748 781646 747298 321288 699819 810014 286344 217787 643101 609052 952728 789220 681529 025841 > 3²⁴⁶ [i]