MinT - Best Known (120−51, 120, s)-Nets in Base 4

Best Known (120−51, 120, s)-Nets in Base 4

(120−51, 120, 130)-Net over F₄ — Constructive and digital

Digital (69, 120, 130)-net over F₄, using

6 times m-reduction [i] based on digital (69, 126, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 63, 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]

(120−51, 120, 156)-Net over F₄ — Digital

Digital (69, 120, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−51, 120, 2470)-Net in Base 4 — Upper bound on s

There is no (69, 120, 2471)-net in base 4, because

1 times m-reduction [i] would yield (69, 119, 2471)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 444533 112357 090477 458056 792704 727991 023395 678889 788503 121119 218415 068408 > 4¹¹⁹ [i]