MinT - Best Known (174−114, 174, s)-Nets in Base 4

Best Known (174−114, 174, s)-Nets in Base 4

(174−114, 174, 66)-Net over F₄ — Constructive and digital

Digital (60, 174, 66)-net over F₄, using

t-expansion [i] based on digital (49, 174, 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]

(174−114, 174, 91)-Net over F₄ — Digital

Digital (60, 174, 91)-net over F₄, using

t-expansion [i] based on digital (50, 174, 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]

(174−114, 174, 461)-Net in Base 4 — Upper bound on s

There is no (60, 174, 462)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 621 963592 104444 299487 201796 113071 861108 502880 785032 566877 052714 619687 837477 925031 018909 933160 784165 595100 > 4¹⁷⁴ [i]