MinT - Best Known (145, 145+50, s)-Nets in Base 4

Best Known (145, 145+50, s)-Nets in Base 4

(145, 145+50, 531)-Net over F₄ — Constructive and digital

Digital (145, 195, 531)-net over F₄, using

12 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(145, 145+50, 648)-Net in Base 4 — Constructive

(145, 195, 648)-net in base 4, using

trace code for nets [i] based on (15, 65, 216)-net in base 64, using
- 5 times m-reduction [i] based on (15, 70, 216)-net in base 64, using
  - base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(145, 145+50, 1610)-Net over F₄ — Digital

Digital (145, 195, 1610)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+50, 168469)-Net in Base 4 — Upper bound on s

There is no (145, 195, 168470)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2522 088751 381473 068257 560866 443094 237421 950650 589346 854792 879027 414763 153693 090503 681167 284565 320622 546251 557167 229248 > 4¹⁹⁵ [i]