MinT - Best Known (236−67, 236, s)-Nets in Base 3

Best Known (236−67, 236, s)-Nets in Base 3

(236−67, 236, 288)-Net over F₃ — Constructive and digital

Digital (169, 236, 288)-net over F₃, using

1 times m-reduction [i] based on digital (169, 237, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 79, 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]

(236−67, 236, 614)-Net over F₃ — Digital

Digital (169, 236, 614)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−67, 236, 16411)-Net in Base 3 — Upper bound on s

There is no (169, 236, 16412)-net in base 3, because

1 times m-reduction [i] would yield (169, 235, 16412)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13303 411381 949502 598981 488654 755878 229966 306642 942485 317844 698116 059730 344546 729605 006015 046626 712108 047905 246265 > 3²³⁵ [i]