MinT - Best Known (90, 90+53, s)-Nets in Base 4

Best Known (90, 90+53, s)-Nets in Base 4

(90, 90+53, 130)-Net over F₄ — Constructive and digital

Digital (90, 143, 130)-net over F₄, using

25 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(90, 90+53, 284)-Net over F₄ — Digital

Digital (90, 143, 284)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+53, 6807)-Net in Base 4 — Upper bound on s

There is no (90, 143, 6808)-net in base 4, because

1 times m-reduction [i] would yield (90, 142, 6808)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 120917 364310 023825 580669 803553 040265 993921 622931 113780 155995 125931 570193 154381 911600 > 4¹⁴² [i]