MinT - Best Known (134, 134+107, s)-Nets in Base 3

Best Known (134, 134+107, s)-Nets in Base 3

(134, 134+107, 128)-Net over F₃ — Constructive and digital

Digital (134, 241, 128)-net over F₃, using

1 times m-reduction [i] based on digital (134, 242, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 121, 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]

(134, 134+107, 164)-Net over F₃ — Digital

Digital (134, 241, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+107, 1438)-Net in Base 3 — Upper bound on s

There is no (134, 241, 1439)-net in base 3, because

1 times m-reduction [i] would yield (134, 240, 1439)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 266034 399052 866158 364650 423449 936864 906422 552563 338870 795970 016914 939795 685220 747749 949508 236077 714778 502784 789975 > 3²⁴⁰ [i]