MinT - Best Known (154−43, 154, s)-Nets in Base 3

Best Known (154−43, 154, s)-Nets in Base 3

(154−43, 154, 252)-Net over F₃ — Constructive and digital

Digital (111, 154, 252)-net over F₃, using

3¹ times duplication [i] based on digital (110, 153, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 51, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(154−43, 154, 454)-Net over F₃ — Digital

Digital (111, 154, 454)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−43, 154, 12970)-Net in Base 3 — Upper bound on s

There is no (111, 154, 12971)-net in base 3, because

1 times m-reduction [i] would yield (111, 153, 12971)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 002803 905738 658884 657967 889561 772841 325873 828458 008740 646377 605623 339503 > 3¹⁵³ [i]