MinT - Best Known (57, 57+88, s)-Nets in Base 4

Best Known (57, 57+88, s)-Nets in Base 4

(57, 57+88, 66)-Net over F₄ — Constructive and digital

Digital (57, 145, 66)-net over F₄, using

t-expansion [i] based on digital (49, 145, 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]

(57, 57+88, 91)-Net over F₄ — Digital

Digital (57, 145, 91)-net over F₄, using

t-expansion [i] based on digital (50, 145, 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]

(57, 57+88, 519)-Net in Base 4 — Upper bound on s

There is no (57, 145, 520)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2126 948023 929536 096213 206403 915887 961713 187146 534219 593308 788854 449391 169648 236924 822208 > 4¹⁴⁵ [i]