MinT - Best Known (174−71, 174, s)-Nets in Base 4

Best Known (174−71, 174, s)-Nets in Base 4

(174−71, 174, 130)-Net over F₄ — Constructive and digital

Digital (103, 174, 130)-net over F₄, using

20 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]

(174−71, 174, 243)-Net over F₄ — Digital

Digital (103, 174, 243)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−71, 174, 4357)-Net in Base 4 — Upper bound on s

There is no (103, 174, 4358)-net in base 4, because

1 times m-reduction [i] would yield (103, 173, 4358)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 144 369403 507308 250560 255917 925303 116648 898643 110959 156881 578546 995278 449322 811335 264327 382851 928761 214800 > 4¹⁷³ [i]