MinT - Best Known (186−47, 186, s)-Nets in Base 3

Best Known (186−47, 186, s)-Nets in Base 3

(186−47, 186, 288)-Net over F₃ — Constructive and digital

Digital (139, 186, 288)-net over F₃, using

6 times m-reduction [i] based on digital (139, 192, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 64, 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]

(186−47, 186, 768)-Net over F₃ — Digital

Digital (139, 186, 768)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−47, 186, 32421)-Net in Base 3 — Upper bound on s

There is no (139, 186, 32422)-net in base 3, because

1 times m-reduction [i] would yield (139, 185, 32422)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18511 364546 633142 148194 615348 926106 267164 788009 556409 991639 562393 530039 748673 800921 824761 > 3¹⁸⁵ [i]