MinT - Best Known (124, 219, s)-Nets in Base 3

Best Known (124, 219, s)-Nets in Base 3

(124, 219, 128)-Net over F₃ — Constructive and digital

Digital (124, 219, 128)-net over F₃, using

3 times m-reduction [i] based on digital (124, 222, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 111, 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]

(124, 219, 161)-Net over F₃ — Digital

Digital (124, 219, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 219, 1454)-Net in Base 3 — Upper bound on s

There is no (124, 219, 1455)-net in base 3, because

1 times m-reduction [i] would yield (124, 218, 1455)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 105 778488 094736 095739 222831 711592 451172 050647 447958 637952 726871 814925 033493 779151 682248 897979 191472 366179 > 3²¹⁸ [i]