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

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

(154−47, 154, 192)-Net over F₃ — Constructive and digital

Digital (107, 154, 192)-net over F₃, using

3¹ times duplication [i] based on digital (106, 153, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 51, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(154−47, 154, 336)-Net over F₃ — Digital

Digital (107, 154, 336)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−47, 154, 7013)-Net in Base 3 — Upper bound on s

There is no (107, 154, 7014)-net in base 3, because

1 times m-reduction [i] would yield (107, 153, 7014)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 008217 718939 483144 901430 596799 869353 743072 767719 317863 716199 249375 116025 > 3¹⁵³ [i]