MinT - Best Known (109−42, 109, s)-Nets in Base 4

Best Known (109−42, 109, s)-Nets in Base 4

(109−42, 109, 130)-Net over F₄ — Constructive and digital

Digital (67, 109, 130)-net over F₄, using

13 times m-reduction [i] based on digital (67, 122, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 61, 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]

(109−42, 109, 199)-Net over F₄ — Digital

Digital (67, 109, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−42, 109, 3840)-Net in Base 4 — Upper bound on s

There is no (67, 109, 3841)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 421444 954577 663610 550903 161994 015481 216007 152511 470889 312772 266496 > 4¹⁰⁹ [i]