MinT - Best Known (152, 190, s)-Nets in Base 4

Best Known (152, 190, s)-Nets in Base 4

(152, 190, 1065)-Net over F₄ — Constructive and digital

Digital (152, 190, 1065)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 34, 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 (118, 156, 1032)-net over F₄, using
  - trace code for nets [i] based on digital (1, 39, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(152, 190, 6050)-Net over F₄ — Digital

Digital (152, 190, 6050)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 190, 2771352)-Net in Base 4 — Upper bound on s

There is no (152, 190, 2771353)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 462634 578007 160341 536718 953585 628121 203019 987368 786859 867196 591587 707289 182734 006532 589294 006541 389136 751862 330504 > 4¹⁹⁰ [i]