MinT - Best Known (244−107, 244, s)-Nets in Base 3

Best Known (244−107, 244, s)-Nets in Base 3

(244−107, 244, 128)-Net over F₃ — Constructive and digital

Digital (137, 244, 128)-net over F₃, using

4 times m-reduction [i] based on digital (137, 248, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 124, 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]

(244−107, 244, 172)-Net over F₃ — Digital

Digital (137, 244, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−107, 244, 1534)-Net in Base 3 — Upper bound on s

There is no (137, 244, 1535)-net in base 3, because

1 times m-reduction [i] would yield (137, 243, 1535)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 89 366412 816768 492061 324344 373976 515171 608174 769036 722422 476384 605091 484415 676091 673507 846668 269389 672773 388456 385431 > 3²⁴³ [i]