MinT - Best Known (154, 154+47, s)-Nets in Base 3

Best Known (154, 154+47, s)-Nets in Base 3

(154, 154+47, 464)-Net over F₃ — Constructive and digital

Digital (154, 201, 464)-net over F₃, using

3¹ times duplication [i] based on digital (153, 200, 464)-net over F₃, using
- t-expansion [i] based on digital (152, 200, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 50, 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]

(154, 154+47, 1117)-Net over F₃ — Digital

Digital (154, 201, 1117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+47, 66398)-Net in Base 3 — Upper bound on s

There is no (154, 201, 66399)-net in base 3, because

1 times m-reduction [i] would yield (154, 200, 66399)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265640 696959 551734 988639 133672 410929 873132 009657 431400 816484 995971 242215 717196 683223 765577 775955 > 3²⁰⁰ [i]