MinT - Best Known (144−53, 144, s)-Nets in Base 3

Best Known (144−53, 144, s)-Nets in Base 3

(144−53, 144, 148)-Net over F₃ — Constructive and digital

Digital (91, 144, 148)-net over F₃, using

4 times m-reduction [i] based on digital (91, 148, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 74, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(144−53, 144, 179)-Net over F₃ — Digital

Digital (91, 144, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−53, 144, 2195)-Net in Base 3 — Upper bound on s

There is no (91, 144, 2196)-net in base 3, because

1 times m-reduction [i] would yield (91, 143, 2196)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 171 138206 813455 309798 973477 784627 071483 890138 810650 534003 251844 601881 > 3¹⁴³ [i]