MinT - Best Known (214−55, 214, s)-Nets in Base 3

Best Known (214−55, 214, s)-Nets in Base 3

(214−55, 214, 288)-Net over F₃ — Constructive and digital

Digital (159, 214, 288)-net over F₃, using

8 times m-reduction [i] based on digital (159, 222, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 74, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(214−55, 214, 807)-Net over F₃ — Digital

Digital (159, 214, 807)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−55, 214, 31693)-Net in Base 3 — Upper bound on s

There is no (159, 214, 31694)-net in base 3, because

1 times m-reduction [i] would yield (159, 213, 31694)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423647 189359 352773 728694 673032 702648 000879 668839 890080 730175 801075 420133 768942 438602 688635 193087 835089 > 3²¹³ [i]