MinT - Best Known (228−76, 228, s)-Nets in Base 3

Best Known (228−76, 228, s)-Nets in Base 3

(228−76, 228, 162)-Net over F₃ — Constructive and digital

Digital (152, 228, 162)-net over F₃, using

12 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 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]

(228−76, 228, 356)-Net over F₃ — Digital

Digital (152, 228, 356)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−76, 228, 5439)-Net in Base 3 — Upper bound on s

There is no (152, 228, 5440)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 115447 029485 432794 600734 476461 580436 057967 385074 988931 234379 799269 976986 623357 826809 523798 619060 069940 053889 > 3²²⁸ [i]