MinT - Best Known (196−54, 196, s)-Nets in Base 3

Best Known (196−54, 196, s)-Nets in Base 3

(196−54, 196, 288)-Net over F₃ — Constructive and digital

Digital (142, 196, 288)-net over F₃, using

3¹ times duplication [i] based on digital (141, 195, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 65, 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]

(196−54, 196, 580)-Net over F₃ — Digital

Digital (142, 196, 580)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−54, 196, 15856)-Net in Base 3 — Upper bound on s

There is no (142, 196, 15857)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3283 681741 069596 606940 271563 207658 589534 093542 347887 832556 374606 516479 705311 028160 336622 462971 > 3¹⁹⁶ [i]