MinT - Best Known (180−72, 180, s)-Nets in Base 3

Best Known (180−72, 180, s)-Nets in Base 3

(180−72, 180, 148)-Net over F₃ — Constructive and digital

Digital (108, 180, 148)-net over F₃, using

2 times m-reduction [i] based on digital (108, 182, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 91, 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]

(180−72, 180, 171)-Net over F₃ — Digital

Digital (108, 180, 171)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−72, 180, 1699)-Net in Base 3 — Upper bound on s

There is no (108, 180, 1700)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 406251 408802 328508 142888 838126 425986 897621 266025 130598 428852 576751 167283 909567 454657 > 3¹⁸⁰ [i]