MinT - Best Known (202−125, 202, s)-Nets in Base 4

Best Known (202−125, 202, s)-Nets in Base 4

(202−125, 202, 104)-Net over F₄ — Constructive and digital

Digital (77, 202, 104)-net over F₄, using

t-expansion [i] based on digital (73, 202, 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]

(202−125, 202, 112)-Net over F₄ — Digital

Digital (77, 202, 112)-net over F₄, using

t-expansion [i] based on digital (73, 202, 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]

(202−125, 202, 664)-Net in Base 4 — Upper bound on s

There is no (77, 202, 665)-net in base 4, because

1 times m-reduction [i] would yield (77, 201, 665)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 059866 444089 920468 296798 494266 713312 518439 901946 212375 431572 750818 135978 485209 961890 279214 495051 812464 659602 101676 645440 > 4²⁰¹ [i]