MinT - Best Known (250−157, 250, s)-Nets in Base 4

Best Known (250−157, 250, s)-Nets in Base 4

(250−157, 250, 104)-Net over F₄ — Constructive and digital

Digital (93, 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]

(250−157, 250, 144)-Net over F₄ — Digital

Digital (93, 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]

(250−157, 250, 768)-Net in Base 4 — Upper bound on s

There is no (93, 250, 769)-net in base 4, because

1 times m-reduction [i] would yield (93, 249, 769)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 826943 262019 848831 973889 690758 526892 754787 183178 149197 519069 130167 184779 351531 369625 429661 551749 888081 834061 336779 789055 260550 496212 907965 320973 285248 > 4²⁴⁹ [i]