MinT - Best Known (173−74, 173, s)-Nets in Base 4

Best Known (173−74, 173, s)-Nets in Base 4

(173−74, 173, 130)-Net over F₄ — Constructive and digital

Digital (99, 173, 130)-net over F₄, using

13 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(173−74, 173, 208)-Net over F₄ — Digital

Digital (99, 173, 208)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−74, 173, 3160)-Net in Base 4 — Upper bound on s

There is no (99, 173, 3161)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 144 932446 893146 718715 766040 395189 667665 409596 273361 179156 227371 464783 899956 108877 311793 181229 284299 741696 > 4¹⁷³ [i]