MinT - Best Known (59, 59+143, s)-Nets in Base 4

Best Known (59, 59+143, s)-Nets in Base 4

(59, 59+143, 66)-Net over F₄ — Constructive and digital

Digital (59, 202, 66)-net over F₄, using

t-expansion [i] based on digital (49, 202, 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]

(59, 59+143, 91)-Net over F₄ — Digital

Digital (59, 202, 91)-net over F₄, using

t-expansion [i] based on digital (50, 202, 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]

(59, 59+143, 404)-Net in Base 4 — Upper bound on s

There is no (59, 202, 405)-net in base 4, because

1 times m-reduction [i] would yield (59, 201, 405)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 701685 136078 022798 156377 915670 505271 090128 200972 795202 935516 104058 839939 130825 141228 756498 498133 053531 437905 769303 907360 > 4²⁰¹ [i]