MinT - Best Known (76, 76+115, s)-Nets in Base 4

Best Known (76, 76+115, s)-Nets in Base 4

(76, 76+115, 104)-Net over F₄ — Constructive and digital

Digital (76, 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]

(76, 76+115, 112)-Net over F₄ — Digital

Digital (76, 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]

(76, 76+115, 701)-Net in Base 4 — Upper bound on s

There is no (76, 191, 702)-net in base 4, because

1 times m-reduction [i] would yield (76, 190, 702)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 497393 661204 895431 102799 954886 998529 688467 796471 474288 212498 741397 086133 527315 110067 589407 885960 313358 337269 869725 > 4¹⁹⁰ [i]