MinT - Best Known (141−64, 141, s)-Nets in Base 4

Best Known (141−64, 141, s)-Nets in Base 4

(141−64, 141, 130)-Net over F₄ — Constructive and digital

Digital (77, 141, 130)-net over F₄, using

1 times m-reduction [i] based on digital (77, 142, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 71, 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]

(141−64, 141, 144)-Net over F₄ — Digital

Digital (77, 141, 144)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−64, 141, 1890)-Net in Base 4 — Upper bound on s

There is no (77, 141, 1891)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 795367 441224 504780 488518 565739 841619 877876 717352 803743 902742 790026 147588 815673 891367 > 4¹⁴¹ [i]