MinT - Best Known (166, 166+84, s)-Nets in Base 3

Best Known (166, 166+84, s)-Nets in Base 3

(166, 166+84, 162)-Net over F₃ — Constructive and digital

Digital (166, 250, 162)-net over F₃, using

t-expansion [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 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]

(166, 166+84, 377)-Net over F₃ — Digital

Digital (166, 250, 377)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+84, 5670)-Net in Base 3 — Upper bound on s

There is no (166, 250, 5671)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191373 677542 637088 683829 573591 922643 623314 006728 886777 432212 024864 309100 587814 166870 838777 702735 800161 586311 924232 295805 > 3²⁵⁰ [i]