MinT - Best Known (121, 171, s)-Nets in Base 4

Best Known (121, 171, s)-Nets in Base 4

(121, 171, 531)-Net over F₄ — Constructive and digital

Digital (121, 171, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 57, 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]

(121, 171, 813)-Net over F₄ — Digital

Digital (121, 171, 813)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 171, 44503)-Net in Base 4 — Upper bound on s

There is no (121, 171, 44504)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 960256 726443 356752 359997 342451 888723 680620 603820 433947 920243 106448 232915 915198 181596 581130 457950 272264 > 4¹⁷¹ [i]