MinT - Best Known (96, 96+75, s)-Nets in Base 4

Best Known (96, 96+75, s)-Nets in Base 4

(96, 96+75, 130)-Net over F₄ — Constructive and digital

Digital (96, 171, 130)-net over F₄, using

9 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(96, 96+75, 190)-Net over F₄ — Digital

Digital (96, 171, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+75, 2820)-Net in Base 4 — Upper bound on s

There is no (96, 171, 2821)-net in base 4, because

1 times m-reduction [i] would yield (96, 170, 2821)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 243011 174683 628741 170668 030373 985200 611436 261853 468597 450703 748738 834427 266038 365907 071083 000487 655200 > 4¹⁷⁰ [i]