MinT - Best Known (195−105, 195, s)-Nets in Base 4

Best Known (195−105, 195, s)-Nets in Base 4

(195−105, 195, 104)-Net over F₄ — Constructive and digital

Digital (90, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(195−105, 195, 129)-Net over F₄ — Digital

Digital (90, 195, 129)-net over F₄, using

t-expansion [i] based on digital (81, 195, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(195−105, 195, 1146)-Net in Base 4 — Upper bound on s

There is no (90, 195, 1147)-net in base 4, because

1 times m-reduction [i] would yield (90, 194, 1147)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 657 570458 855950 591036 220899 803657 585189 595096 796405 845669 237217 814383 284827 691291 561812 461316 441614 329715 509087 266010 > 4¹⁹⁴ [i]