MinT - Best Known (194−91, 194, s)-Nets in Base 4

Best Known (194−91, 194, s)-Nets in Base 4

(194−91, 194, 130)-Net over F₄ — Constructive and digital

Digital (103, 194, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 97, 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]

(194−91, 194, 171)-Net over F₄ — Digital

Digital (103, 194, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−91, 194, 2208)-Net in Base 4 — Upper bound on s

There is no (103, 194, 2209)-net in base 4, because

1 times m-reduction [i] would yield (103, 193, 2209)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 159 981449 805741 202202 336859 561347 525498 676558 358317 981521 921313 270622 552734 895492 887076 270427 739069 569791 949537 308672 > 4¹⁹³ [i]