MinT - Best Known (206−59, 206, s)-Nets in Base 4

Best Known (206−59, 206, s)-Nets in Base 4

(206−59, 206, 531)-Net over F₄ — Constructive and digital

Digital (147, 206, 531)-net over F₄, using

4 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(206−59, 206, 1036)-Net over F₄ — Digital

Digital (147, 206, 1036)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−59, 206, 70112)-Net in Base 4 — Upper bound on s

There is no (147, 206, 70113)-net in base 4, because

1 times m-reduction [i] would yield (147, 205, 70113)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 755584 552437 033461 770111 718422 452925 337090 211176 540248 295412 736741 811405 879842 275919 030901 983131 126260 301466 462067 677056 > 4²⁰⁵ [i]