MinT - Best Known (52, 52+56, s)-Nets in Base 4

Best Known (52, 52+56, s)-Nets in Base 4

(52, 52+56, 66)-Net over F₄ — Constructive and digital

Digital (52, 108, 66)-net over F₄, using

t-expansion [i] based on digital (49, 108, 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]

(52, 52+56, 91)-Net over F₄ — Digital

Digital (52, 108, 91)-net over F₄, using

t-expansion [i] based on digital (50, 108, 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]

(52, 52+56, 768)-Net in Base 4 — Upper bound on s

There is no (52, 108, 769)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 107935 734362 473213 344269 827923 466884 741965 927892 322373 052780 668608 > 4¹⁰⁸ [i]