MinT - Best Known (221−78, 221, s)-Nets in Base 3

Best Known (221−78, 221, s)-Nets in Base 3

(221−78, 221, 162)-Net over F₃ — Constructive and digital

Digital (143, 221, 162)-net over F₃, using

1 times m-reduction [i] based on digital (143, 222, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 111, 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]

(221−78, 221, 292)-Net over F₃ — Digital

Digital (143, 221, 292)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−78, 221, 3852)-Net in Base 3 — Upper bound on s

There is no (143, 221, 3853)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2782 662656 525452 360353 100981 408182 039896 850511 380270 273442 034239 481685 442285 658838 606506 471585 813396 095611 > 3²²¹ [i]