MinT - Best Known (201−125, 201, s)-Nets in Base 4

Best Known (201−125, 201, s)-Nets in Base 4

(201−125, 201, 104)-Net over F₄ — Constructive and digital

Digital (76, 201, 104)-net over F₄, using

t-expansion [i] based on digital (73, 201, 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]

(201−125, 201, 112)-Net over F₄ — Digital

Digital (76, 201, 112)-net over F₄, using

t-expansion [i] based on digital (73, 201, 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]

(201−125, 201, 648)-Net in Base 4 — Upper bound on s

There is no (76, 201, 649)-net in base 4, because

1 times m-reduction [i] would yield (76, 200, 649)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 710534 773145 698721 314334 891672 108453 682057 673448 867271 821629 878068 195901 121582 537532 553796 230437 769692 824031 719007 839040 > 4²⁰⁰ [i]