MinT - Best Known (174−95, 174, s)-Nets in Base 4

Best Known (174−95, 174, s)-Nets in Base 4

(174−95, 174, 104)-Net over F₄ — Constructive and digital

Digital (79, 174, 104)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−95, 174, 112)-Net over F₄ — Digital

Digital (79, 174, 112)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−95, 174, 968)-Net in Base 4 — Upper bound on s

There is no (79, 174, 969)-net in base 4, because

1 times m-reduction [i] would yield (79, 173, 969)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 429927 066563 368972 521387 637566 784142 255273 382184 675164 510725 454773 513579 563592 448384 889779 265815 959360 > 4¹⁷³ [i]