MinT - Best Known (77, 138, s)-Nets in Base 4

Best Known (77, 138, s)-Nets in Base 4

(77, 138, 130)-Net over F₄ — Constructive and digital

Digital (77, 138, 130)-net over F₄, using

4 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]

(77, 138, 154)-Net over F₄ — Digital

Digital (77, 138, 154)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 138, 2230)-Net in Base 4 — Upper bound on s

There is no (77, 138, 2231)-net in base 4, because

1 times m-reduction [i] would yield (77, 137, 2231)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30667 246142 510797 530055 871290 524963 175490 180529 019009 934951 178395 241415 032578 234212 > 4¹³⁷ [i]