MinT - Best Known (235−89, 235, s)-Nets in Base 3

Best Known (235−89, 235, s)-Nets in Base 3

(235−89, 235, 156)-Net over F₃ — Constructive and digital

Digital (146, 235, 156)-net over F₃, using

13 times m-reduction [i] based on digital (146, 248, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 124, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(235−89, 235, 252)-Net over F₃ — Digital

Digital (146, 235, 252)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−89, 235, 2930)-Net in Base 3 — Upper bound on s

There is no (146, 235, 2931)-net in base 3, because

1 times m-reduction [i] would yield (146, 234, 2931)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4459 054563 955419 346995 373913 276261 564374 702501 713116 711832 774455 375312 076228 397843 704804 342817 738272 964400 924937 > 3²³⁴ [i]