MinT - Best Known (215−55, 215, s)-Nets in Base 3

Best Known (215−55, 215, s)-Nets in Base 3

(215−55, 215, 288)-Net over F₃ — Constructive and digital

Digital (160, 215, 288)-net over F₃, using

t-expansion [i] based on digital (159, 215, 288)-net over F₃, using
- 7 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]

(215−55, 215, 824)-Net over F₃ — Digital

Digital (160, 215, 824)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−55, 215, 33010)-Net in Base 3 — Upper bound on s

There is no (160, 215, 33011)-net in base 3, because

1 times m-reduction [i] would yield (160, 214, 33011)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 270625 875240 751818 009062 764012 783589 509968 605354 568891 128069 731847 427444 575984 676706 926222 014648 041147 > 3²¹⁴ [i]