MinT - Best Known (54, 54+104, s)-Nets in Base 4

Best Known (54, 54+104, s)-Nets in Base 4

(54, 54+104, 66)-Net over F₄ — Constructive and digital

Digital (54, 158, 66)-net over F₄, using

t-expansion [i] based on digital (49, 158, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(54, 54+104, 91)-Net over F₄ — Digital

Digital (54, 158, 91)-net over F₄, using

t-expansion [i] based on digital (50, 158, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(54, 54+104, 413)-Net in Base 4 — Upper bound on s

There is no (54, 158, 414)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 137506 583580 099398 783723 592902 618288 461685 521704 652875 244301 837209 594177 531599 501443 206404 834700 > 4¹⁵⁸ [i]