MinT - Best Known (217−59, 217, s)-Nets in Base 3

Best Known (217−59, 217, s)-Nets in Base 3

(217−59, 217, 288)-Net over F₃ — Constructive and digital

Digital (158, 217, 288)-net over F₃, using

t-expansion [i] based on digital (157, 217, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 73, 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]

(217−59, 217, 663)-Net over F₃ — Digital

Digital (158, 217, 663)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−59, 217, 20855)-Net in Base 3 — Upper bound on s

There is no (158, 217, 20856)-net in base 3, because

1 times m-reduction [i] would yield (158, 216, 20856)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 434564 850408 509831 508558 531872 398119 098250 316245 663445 206954 798988 895746 129691 180138 108636 070401 984241 > 3²¹⁶ [i]