MinT - Best Known (151, 232, s)-Nets in Base 3

Best Known (151, 232, s)-Nets in Base 3

(151, 232, 162)-Net over F₃ — Constructive and digital

Digital (151, 232, 162)-net over F₃, using

6 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]

(151, 232, 315)-Net over F₃ — Digital

Digital (151, 232, 315)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 232, 4449)-Net in Base 3 — Upper bound on s

There is no (151, 232, 4450)-net in base 3, because

1 times m-reduction [i] would yield (151, 231, 4450)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 783970 659870 515207 400943 897710 862079 450283 750264 096250 637659 537817 220686 775046 780294 985651 516234 003232 275857 > 3²³¹ [i]