MinT - Best Known (157, 157+68, s)-Nets in Base 4

Best Known (157, 157+68, s)-Nets in Base 4

(157, 157+68, 531)-Net over F₄ — Constructive and digital

Digital (157, 225, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 75, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(157, 157+68, 890)-Net over F₄ — Digital

Digital (157, 225, 890)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+68, 43480)-Net in Base 4 — Upper bound on s

There is no (157, 225, 43481)-net in base 4, because

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]