MinT - Best Known (181−121, 181, s)-Nets in Base 4

Best Known (181−121, 181, s)-Nets in Base 4

(181−121, 181, 66)-Net over F₄ — Constructive and digital

Digital (60, 181, 66)-net over F₄, using

t-expansion [i] based on digital (49, 181, 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]

(181−121, 181, 91)-Net over F₄ — Digital

Digital (60, 181, 91)-net over F₄, using

t-expansion [i] based on digital (50, 181, 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]

(181−121, 181, 447)-Net in Base 4 — Upper bound on s

There is no (60, 181, 448)-net in base 4, because

1 times m-reduction [i] would yield (60, 180, 448)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 633205 181984 069008 847964 349800 343843 378939 889104 556617 325900 439097 076692 647879 437028 629099 740622 843355 760883 > 4¹⁸⁰ [i]