MinT - Best Known (145, 145+36, s)-Nets in Base 4

Best Known (145, 145+36, s)-Nets in Base 4

(145, 145+36, 1065)-Net over F₄ — Constructive and digital

Digital (145, 181, 1065)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 33, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (112, 148, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 37, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(145, 145+36, 6038)-Net over F₄ — Digital

Digital (145, 181, 6038)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+36, 2851374)-Net in Base 4 — Upper bound on s

There is no (145, 181, 2851375)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 394191 152329 377754 024762 844038 618413 542783 706668 137816 798705 727416 624164 623705 566611 500975 002435 544618 821726 > 4¹⁸¹ [i]