MinT - Best Known (219−126, 219, s)-Nets in Base 4

Best Known (219−126, 219, s)-Nets in Base 4

(219−126, 219, 104)-Net over F₄ — Constructive and digital

Digital (93, 219, 104)-net over F₄, using

t-expansion [i] based on digital (73, 219, 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]

(219−126, 219, 144)-Net over F₄ — Digital

Digital (93, 219, 144)-net over F₄, using

t-expansion [i] based on digital (91, 219, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(219−126, 219, 952)-Net in Base 4 — Upper bound on s

There is no (93, 219, 953)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 742313 580764 583491 487528 621311 108841 512254 567968 612750 922977 458737 576373 969269 088041 370189 030843 011201 617691 957872 208265 316315 414400 > 4²¹⁹ [i]