MinT - Best Known (208−63, 208, s)-Nets in Base 4

Best Known (208−63, 208, s)-Nets in Base 4

(208−63, 208, 450)-Net over F₄ — Constructive and digital

Digital (145, 208, 450)-net over F₄, using

2 times m-reduction [i] based on digital (145, 210, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 105, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(208−63, 208, 825)-Net over F₄ — Digital

Digital (145, 208, 825)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−63, 208, 43337)-Net in Base 4 — Upper bound on s

There is no (145, 208, 43338)-net in base 4, because

1 times m-reduction [i] would yield (145, 207, 43338)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42319 233212 490372 429995 424595 798348 920044 466284 421337 873561 915570 424986 612936 498598 073158 320821 833485 626198 405992 479948 913440 > 4²⁰⁷ [i]