MinT - Best Known (153−53, 153, s)-Nets in Base 3

Best Known (153−53, 153, s)-Nets in Base 3

(153−53, 153, 156)-Net over F₃ — Constructive and digital

Digital (100, 153, 156)-net over F₃, using

3 times m-reduction [i] based on digital (100, 156, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 78, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(153−53, 153, 226)-Net over F₃ — Digital

Digital (100, 153, 226)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−53, 153, 3222)-Net in Base 3 — Upper bound on s

There is no (100, 153, 3223)-net in base 3, because

1 times m-reduction [i] would yield (100, 152, 3223)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 346769 953174 328169 947571 518762 333848 310790 423522 544984 924418 580947 097213 > 3¹⁵² [i]