MinT - Best Known (69, 69+54, s)-Nets in Base 4

Best Known (69, 69+54, s)-Nets in Base 4

(69, 69+54, 130)-Net over F₄ — Constructive and digital

Digital (69, 123, 130)-net over F₄, using

3 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]

(69, 69+54, 143)-Net over F₄ — Digital

Digital (69, 123, 143)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+54, 1991)-Net in Base 4 — Upper bound on s

There is no (69, 123, 1992)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 334217 465694 579005 999086 947517 018945 595286 508406 442597 560767 522710 391880 > 4¹²³ [i]