MinT - Best Known (77, 77+114, s)-Nets in Base 4

Best Known (77, 77+114, s)-Nets in Base 4

(77, 77+114, 104)-Net over F₄ — Constructive and digital

Digital (77, 191, 104)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(77, 77+114, 112)-Net over F₄ — Digital

Digital (77, 191, 112)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(77, 77+114, 720)-Net in Base 4 — Upper bound on s

There is no (77, 191, 721)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 455766 621785 007694 121359 882732 530456 466904 431118 034291 909870 515303 533116 529846 978003 719559 171132 417517 805966 001440 > 4¹⁹¹ [i]