MinT - Best Known (194−90, 194, s)-Nets in Base 4

Best Known (194−90, 194, s)-Nets in Base 4

(194−90, 194, 130)-Net over F₄ — Constructive and digital

Digital (104, 194, 130)-net over F₄, using

2 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]

(194−90, 194, 177)-Net over F₄ — Digital

Digital (104, 194, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−90, 194, 2278)-Net in Base 4 — Upper bound on s

There is no (104, 194, 2279)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 636 773790 518424 199141 395294 381884 651974 147561 904749 875513 640069 538930 858690 106580 125571 151713 845039 838503 317932 033072 > 4¹⁹⁴ [i]