MinT - Best Known (144, 144+74, s)-Nets in Base 3

Best Known (144, 144+74, s)-Nets in Base 3

(144, 144+74, 162)-Net over F₃ — Constructive and digital

Digital (144, 218, 162)-net over F₃, using

6 times m-reduction [i] based on digital (144, 224, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 112, 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]

(144, 144+74, 324)-Net over F₃ — Digital

Digital (144, 218, 324)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+74, 4706)-Net in Base 3 — Upper bound on s

There is no (144, 218, 4707)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 427672 577913 125871 851096 402290 246100 555373 954992 940092 622942 344150 949986 714680 765267 890766 208567 984639 > 3²¹⁸ [i]