MinT - Best Known (157, 157+92, s)-Nets in Base 3

Best Known (157, 157+92, s)-Nets in Base 3

(157, 157+92, 162)-Net over F₃ — Constructive and digital

Digital (157, 249, 162)-net over F₃, using

1 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 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]

(157, 157+92, 285)-Net over F₃ — Digital

Digital (157, 249, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+92, 3397)-Net in Base 3 — Upper bound on s

There is no (157, 249, 3398)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64175 415257 565451 697033 979816 615380 328490 224263 232664 221916 007515 376357 158087 559594 037908 456521 515295 115457 490498 950821 > 3²⁴⁹ [i]