MinT - Best Known (196−92, 196, s)-Nets in Base 4

Best Known (196−92, 196, s)-Nets in Base 4

(196−92, 196, 130)-Net over F₄ — Constructive and digital

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]

(196−92, 196, 172)-Net over F₄ — Digital

Digital (104, 196, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−92, 196, 2167)-Net in Base 4 — Upper bound on s

There is no (104, 196, 2168)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10212 257115 414645 905615 852642 586257 861738 197251 069113 090261 001937 461888 475184 838542 691531 487754 980808 452216 692044 740870 > 4¹⁹⁶ [i]