MinT - Best Known (180−75, 180, s)-Nets in Base 3

Best Known (180−75, 180, s)-Nets in Base 3

(180−75, 180, 128)-Net over F₃ — Constructive and digital

Digital (105, 180, 128)-net over F₃, using

4 times m-reduction [i] based on digital (105, 184, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 92, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(180−75, 180, 152)-Net over F₃ — Digital

Digital (105, 180, 152)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−75, 180, 1453)-Net in Base 3 — Upper bound on s

There is no (105, 180, 1454)-net in base 3, because

1 times m-reduction [i] would yield (105, 179, 1454)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 626235 925753 574623 407204 024385 473595 948301 014983 461790 627242 541736 911254 221297 391797 > 3¹⁷⁹ [i]