MinT - Best Known (157, 157+69, s)-Nets in Base 4

Best Known (157, 157+69, s)-Nets in Base 4

(157, 157+69, 450)-Net over F₄ — Constructive and digital

Digital (157, 226, 450)-net over F₄, using

8 times m-reduction [i] based on digital (157, 234, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 117, 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]

(157, 157+69, 857)-Net over F₄ — Digital

Digital (157, 226, 857)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+69, 43480)-Net in Base 4 — Upper bound on s

There is no (157, 226, 43481)-net in base 4, because

1 times m-reduction [i] would yield (157, 225, 43481)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2907 961359 248687 957928 272318 580725 752122 358103 067488 033496 294638 361993 288268 524653 414650 028333 399793 425560 720469 000093 804718 738140 817592 > 4²²⁵ [i]