MinT - Best Known (144−45, 144, s)-Nets in Base 3

Best Known (144−45, 144, s)-Nets in Base 3

(144−45, 144, 156)-Net over F₃ — Constructive and digital

Digital (99, 144, 156)-net over F₃, using

10 times m-reduction [i] based on digital (99, 154, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 77, 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]

(144−45, 144, 294)-Net over F₃ — Digital

Digital (99, 144, 294)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−45, 144, 5694)-Net in Base 3 — Upper bound on s

There is no (99, 144, 5695)-net in base 3, because

1 times m-reduction [i] would yield (99, 143, 5695)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 317350 038904 208465 876793 356334 381444 109066 107542 915276 162596 069973 > 3¹⁴³ [i]