MinT - Best Known (180−70, 180, s)-Nets in Base 3

Best Known (180−70, 180, s)-Nets in Base 3

(180−70, 180, 148)-Net over F₃ — Constructive and digital

Digital (110, 180, 148)-net over F₃, using

6 times m-reduction [i] based on digital (110, 186, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 93, 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]

(180−70, 180, 185)-Net over F₃ — Digital

Digital (110, 180, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−70, 180, 1942)-Net in Base 3 — Upper bound on s

There is no (110, 180, 1943)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 556171 885654 378508 735026 013469 133110 879562 529111 352901 021566 801519 085575 472622 089499 > 3¹⁸⁰ [i]