MinT - Best Known (247−93, 247, s)-Nets in Base 3

Best Known (247−93, 247, s)-Nets in Base 3

(247−93, 247, 156)-Net over F₃ — Constructive and digital

Digital (154, 247, 156)-net over F₃, using

t-expansion [i] based on digital (147, 247, 156)-net over F₃, using
- 3 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]

(247−93, 247, 267)-Net over F₃ — Digital

Digital (154, 247, 267)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−93, 247, 3159)-Net in Base 3 — Upper bound on s

There is no (154, 247, 3160)-net in base 3, because

1 times m-reduction [i] would yield (154, 246, 3160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2378 750543 663351 060536 483099 542309 961454 074725 923403 397907 235471 706622 070689 899152 607442 737463 208412 868291 459886 567825 > 3²⁴⁶ [i]