MinT - Best Known (174−72, 174, s)-Nets in Base 4

Best Known (174−72, 174, s)-Nets in Base 4

(174−72, 174, 130)-Net over F₄ — Constructive and digital

Digital (102, 174, 130)-net over F₄, using

18 times m-reduction [i] based on digital (102, 192, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 96, 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]

(174−72, 174, 232)-Net over F₄ — Digital

Digital (102, 174, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−72, 174, 3839)-Net in Base 4 — Upper bound on s

There is no (102, 174, 3840)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 576 842629 726969 682852 651556 002875 594236 862346 731577 568274 891385 544096 108015 762804 272991 279831 263026 177369 > 4¹⁷⁴ [i]