MinT - Best Known (193−89, 193, s)-Nets in Base 4

Best Known (193−89, 193, s)-Nets in Base 4

(193−89, 193, 130)-Net over F₄ — Constructive and digital

Digital (104, 193, 130)-net over F₄, using

3 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]

(193−89, 193, 180)-Net over F₄ — Digital

Digital (104, 193, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−89, 193, 2401)-Net in Base 4 — Upper bound on s

There is no (104, 193, 2402)-net in base 4, because

1 times m-reduction [i] would yield (104, 192, 2402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 621131 837548 204789 862992 539120 854190 302528 859585 892157 127294 531074 813631 412913 490623 486088 991549 087019 996290 861552 > 4¹⁹² [i]