MinT - Best Known (176−100, 176, s)-Nets in Base 4

Best Known (176−100, 176, s)-Nets in Base 4

(176−100, 176, 104)-Net over F₄ — Constructive and digital

Digital (76, 176, 104)-net over F₄, using

t-expansion [i] based on digital (73, 176, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(176−100, 176, 112)-Net over F₄ — Digital

Digital (76, 176, 112)-net over F₄, using

t-expansion [i] based on digital (73, 176, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(176−100, 176, 814)-Net in Base 4 — Upper bound on s

There is no (76, 176, 815)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9597 256800 301129 650205 732327 996860 481866 904594 150992 857959 760569 356732 867345 181308 476518 106949 429164 022448 > 4¹⁷⁶ [i]