MinT - Best Known (185−81, 185, s)-Nets in Base 4

Best Known (185−81, 185, s)-Nets in Base 4

(185−81, 185, 130)-Net over F₄ — Constructive and digital

Digital (104, 185, 130)-net over F₄, using

11 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(185−81, 185, 204)-Net over F₄ — Digital

Digital (104, 185, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−81, 185, 3058)-Net in Base 4 — Upper bound on s

There is no (104, 185, 3059)-net in base 4, because

1 times m-reduction [i] would yield (104, 184, 3059)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 604 089493 895463 314873 207353 528107 401087 148362 354169 420254 974976 482156 477069 372277 127540 875515 489865 490321 644230 > 4¹⁸⁴ [i]