MinT - Best Known (76, 76+44, s)-Nets in Base 4

Best Known (76, 76+44, s)-Nets in Base 4

(76, 76+44, 130)-Net over F₄ — Constructive and digital

Digital (76, 120, 130)-net over F₄, using

20 times m-reduction [i] based on digital (76, 140, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 70, 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]

(76, 76+44, 255)-Net over F₄ — Digital

Digital (76, 120, 255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+44, 5785)-Net in Base 4 — Upper bound on s

There is no (76, 120, 5786)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 768458 006295 617036 357434 288939 484533 898320 561899 824679 651267 523379 381676 > 4¹²⁰ [i]