MinT - Best Known (173−115, 173, s)-Nets in Base 4

Best Known (173−115, 173, s)-Nets in Base 4

(173−115, 173, 66)-Net over F₄ — Constructive and digital

Digital (58, 173, 66)-net over F₄, using

t-expansion [i] based on digital (49, 173, 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]

(173−115, 173, 91)-Net over F₄ — Digital

Digital (58, 173, 91)-net over F₄, using

t-expansion [i] based on digital (50, 173, 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]

(173−115, 173, 437)-Net in Base 4 — Upper bound on s

There is no (58, 173, 438)-net in base 4, because

1 times m-reduction [i] would yield (58, 172, 438)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38 943876 408716 291772 749181 828038 028790 628056 195991 088301 942725 909466 455887 992983 435951 167023 416856 361200 > 4¹⁷² [i]