MinT - Best Known (50, 50+84, s)-Nets in Base 4

Best Known (50, 50+84, s)-Nets in Base 4

(50, 50+84, 66)-Net over F₄ — Constructive and digital

Digital (50, 134, 66)-net over F₄, using

t-expansion [i] based on digital (49, 134, 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]

(50, 50+84, 91)-Net over F₄ — Digital

Digital (50, 134, 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]

(50, 50+84, 425)-Net in Base 4 — Upper bound on s

There is no (50, 134, 426)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 511 910810 178112 258574 508334 109747 659432 473370 998453 513663 702936 331771 507388 522920 > 4¹³⁴ [i]