MinT - Best Known (65, 65+26, s)-Nets in Base 3

Best Known (65, 65+26, s)-Nets in Base 3

(65, 65+26, 192)-Net over F₃ — Constructive and digital

Digital (65, 91, 192)-net over F₃, using

3¹ times duplication [i] based on digital (64, 90, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 30, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(65, 65+26, 282)-Net over F₃ — Digital

Digital (65, 91, 282)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+26, 6185)-Net in Base 3 — Upper bound on s

There is no (65, 91, 6186)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 231666 637272 623422 728411 701423 168657 547229 > 3⁹¹ [i]