MinT - Best Known (187−84, 187, s)-Nets in Base 4

Best Known (187−84, 187, s)-Nets in Base 4

(187−84, 187, 130)-Net over F₄ — Constructive and digital

Digital (103, 187, 130)-net over F₄, using

7 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(187−84, 187, 190)-Net over F₄ — Digital

Digital (103, 187, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−84, 187, 2603)-Net in Base 4 — Upper bound on s

There is no (103, 187, 2604)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38656 786464 511567 452061 684787 050265 630908 857736 078164 079908 196240 514672 506261 840176 497736 177163 438977 898916 853835 > 4¹⁸⁷ [i]