MinT - Best Known (167, 167+54, s)-Nets in Base 3

Best Known (167, 167+54, s)-Nets in Base 3

(167, 167+54, 400)-Net over F₃ — Constructive and digital

Digital (167, 221, 400)-net over F₃, using

3¹ times duplication [i] based on digital (166, 220, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 55, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(167, 167+54, 1010)-Net over F₃ — Digital

Digital (167, 221, 1010)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+54, 43897)-Net in Base 3 — Upper bound on s

There is no (167, 221, 43898)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2779 134880 852798 953200 407500 817692 843529 187506 838817 436395 808590 726925 234569 310191 856846 181312 551189 605121 > 3²²¹ [i]