MinT - Best Known (173−78, 173, s)-Nets in Base 4

Best Known (173−78, 173, s)-Nets in Base 4

(173−78, 173, 130)-Net over F₄ — Constructive and digital

Digital (95, 173, 130)-net over F₄, using

5 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(173−78, 173, 175)-Net over F₄ — Digital

Digital (95, 173, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−78, 173, 2372)-Net in Base 4 — Upper bound on s

There is no (95, 173, 2373)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 144 707211 754659 714433 954073 712384 684779 252433 128955 980293 099581 725230 598403 858097 828206 408316 245979 832896 > 4¹⁷³ [i]