MinT - Best Known (75, 75+105, s)-Nets in Base 4

Best Known (75, 75+105, s)-Nets in Base 4

(75, 75+105, 104)-Net over F₄ — Constructive and digital

Digital (75, 180, 104)-net over F₄, using

t-expansion [i] based on digital (73, 180, 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]

(75, 75+105, 112)-Net over F₄ — Digital

Digital (75, 180, 112)-net over F₄, using

t-expansion [i] based on digital (73, 180, 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]

(75, 75+105, 754)-Net in Base 4 — Upper bound on s

There is no (75, 180, 755)-net in base 4, because

1 times m-reduction [i] would yield (75, 179, 755)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 600952 213903 342375 037867 447414 658570 927544 377774 617229 505746 107815 859136 625103 779941 763757 903621 414580 392176 > 4¹⁷⁹ [i]