MinT - Best Known (175−77, 175, s)-Nets in Base 4

Best Known (175−77, 175, s)-Nets in Base 4

(175−77, 175, 130)-Net over F₄ — Constructive and digital

Digital (98, 175, 130)-net over F₄, using

9 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(175−77, 175, 192)-Net over F₄ — Digital

Digital (98, 175, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−77, 175, 2829)-Net in Base 4 — Upper bound on s

There is no (98, 175, 2830)-net in base 4, because

1 times m-reduction [i] would yield (98, 174, 2830)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 575 413953 602184 750370 040521 059289 416911 897716 278225 271185 083839 226934 250295 211434 035342 212044 713289 535328 > 4¹⁷⁴ [i]