MinT - Best Known (109−43, 109, s)-Nets in Base 4

Best Known (109−43, 109, s)-Nets in Base 4

(109−43, 109, 130)-Net over F₄ — Constructive and digital

Digital (66, 109, 130)-net over F₄, using

11 times m-reduction [i] based on digital (66, 120, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 60, 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]

(109−43, 109, 185)-Net over F₄ — Digital

Digital (66, 109, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−43, 109, 3594)-Net in Base 4 — Upper bound on s

There is no (66, 109, 3595)-net in base 4, because

1 times m-reduction [i] would yield (66, 108, 3595)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 105639 695392 191386 857295 286230 971754 704154 700252 345100 936977 549184 > 4¹⁰⁸ [i]