MinT - Best Known (214−52, 214, s)-Nets in Base 3

Best Known (214−52, 214, s)-Nets in Base 3

(214−52, 214, 400)-Net over F₃ — Constructive and digital

Digital (162, 214, 400)-net over F₃, using

3² times duplication [i] based on digital (160, 212, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 53, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(214−52, 214, 1006)-Net over F₃ — Digital

Digital (162, 214, 1006)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−52, 214, 44574)-Net in Base 3 — Upper bound on s

There is no (162, 214, 44575)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 270551 377988 158198 343262 724829 859337 488587 756197 440614 271994 049109 861595 899326 382252 094039 144687 750157 > 3²¹⁴ [i]