MinT - Best Known (240−79, 240, s)-Nets in Base 4

Best Known (240−79, 240, s)-Nets in Base 4

(240−79, 240, 450)-Net over F₄ — Constructive and digital

Digital (161, 240, 450)-net over F₄, using

2 times m-reduction [i] based on digital (161, 242, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 121, 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]

(240−79, 240, 676)-Net over F₄ — Digital

Digital (161, 240, 676)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−79, 240, 25078)-Net in Base 4 — Upper bound on s

There is no (161, 240, 25079)-net in base 4, because

1 times m-reduction [i] would yield (161, 239, 25079)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 781321 240458 904707 106154 214921 733745 679518 669043 791863 289289 242498 677955 919903 329639 642011 560666 318207 851012 371174 371977 348088 416287 241590 378252 > 4²³⁹ [i]