MinT - Best Known (240−78, 240, s)-Nets in Base 4

Best Known (240−78, 240, s)-Nets in Base 4

(240−78, 240, 450)-Net over F₄ — Constructive and digital

Digital (162, 240, 450)-net over F₄, using

4 times m-reduction [i] based on digital (162, 244, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 122, 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]

(240−78, 240, 709)-Net over F₄ — Digital

Digital (162, 240, 709)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−78, 240, 25986)-Net in Base 4 — Upper bound on s

There is no (162, 240, 25987)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 122248 624454 327159 843407 810317 767214 781874 427268 835501 629984 266529 683424 091632 416490 550136 336527 823669 395601 655664 435568 378429 816187 460294 186752 > 4²⁴⁰ [i]