MinT - Best Known (242−81, 242, s)-Nets in Base 4

Best Known (242−81, 242, s)-Nets in Base 4

(242−81, 242, 450)-Net over F₄ — Constructive and digital

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]

(242−81, 242, 641)-Net over F₄ — Digital

Digital (161, 242, 641)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−81, 242, 22255)-Net in Base 4 — Upper bound on s

There is no (161, 242, 22256)-net in base 4, because

1 times m-reduction [i] would yield (161, 241, 22256)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 493500 839803 389377 437249 730841 928738 934864 273566 328996 682644 670549 645330 981959 997767 224846 766429 709581 576765 705457 651442 391806 759366 812135 174817 > 4²⁴¹ [i]