MinT - Best Known (235−84, 235, s)-Nets in Base 3

Best Known (235−84, 235, s)-Nets in Base 3

(235−84, 235, 162)-Net over F₃ — Constructive and digital

Digital (151, 235, 162)-net over F₃, using

3 times m-reduction [i] based on digital (151, 238, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 119, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(235−84, 235, 297)-Net over F₃ — Digital

Digital (151, 235, 297)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−84, 235, 3816)-Net in Base 3 — Upper bound on s

There is no (151, 235, 3817)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13313 216354 210338 666406 408584 392061 172933 017736 622761 130506 752345 715926 836976 625286 733083 700205 859649 299314 949945 > 3²³⁵ [i]