MinT - Best Known (250−155, 250, s)-Nets in Base 4

Best Known (250−155, 250, s)-Nets in Base 4

(250−155, 250, 104)-Net over F₄ — Constructive and digital

Digital (95, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(250−155, 250, 144)-Net over F₄ — Digital

Digital (95, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−155, 250, 807)-Net in Base 4 — Upper bound on s

There is no (95, 250, 808)-net in base 4, because

1 times m-reduction [i] would yield (95, 249, 808)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 827304 795821 221480 067509 546348 747850 725648 663180 750235 155422 726746 368098 803052 306770 856431 091094 424670 238247 579759 132631 344765 857600 417233 668203 521520 > 4²⁴⁹ [i]