MinT - Best Known (134, 134+65, s)-Nets in Base 3

Best Known (134, 134+65, s)-Nets in Base 3

(134, 134+65, 162)-Net over F₃ — Constructive and digital

Digital (134, 199, 162)-net over F₃, using

5 times m-reduction [i] based on digital (134, 204, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 102, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(134, 134+65, 338)-Net over F₃ — Digital

Digital (134, 199, 338)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+65, 5697)-Net in Base 3 — Upper bound on s

There is no (134, 199, 5698)-net in base 3, because

1 times m-reduction [i] would yield (134, 198, 5698)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29672 100143 060205 264032 977906 130952 582321 418219 875256 309841 106545 451543 676420 379377 737366 264129 > 3¹⁹⁸ [i]