MinT - Best Known (129, 129+64, s)-Nets in Base 3

Best Known (129, 129+64, s)-Nets in Base 3

(129, 129+64, 162)-Net over F₃ — Constructive and digital

Digital (129, 193, 162)-net over F₃, using

1 times m-reduction [i] based on digital (129, 194, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 97, 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]

(129, 129+64, 314)-Net over F₃ — Digital

Digital (129, 193, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+64, 4793)-Net in Base 3 — Upper bound on s

There is no (129, 193, 4794)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 869716 423871 246282 668178 689258 649813 518597 423062 597921 170266 918873 792768 046213 022863 881025 > 3¹⁹³ [i]