MinT - Best Known (169, 169+52, s)-Nets in Base 3

Best Known (169, 169+52, s)-Nets in Base 3

(169, 169+52, 464)-Net over F₃ — Constructive and digital

Digital (169, 221, 464)-net over F₃, using

3¹ times duplication [i] based on digital (168, 220, 464)-net over F₃, using
- t-expansion [i] based on digital (167, 220, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 55, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(169, 169+52, 1180)-Net over F₃ — Digital

Digital (169, 221, 1180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+52, 59925)-Net in Base 3 — Upper bound on s

There is no (169, 221, 59926)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2779 466238 585328 325177 261457 476654 328424 271867 688642 245836 666309 519203 244839 220314 300781 721290 424156 646141 > 3²²¹ [i]