MinT - Best Known (250−115, 250, s)-Nets in Base 4

Best Known (250−115, 250, s)-Nets in Base 4

(250−115, 250, 130)-Net over F₄ — Constructive and digital

Digital (135, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(250−115, 250, 228)-Net over F₄ — Digital

Digital (135, 250, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−115, 250, 3093)-Net in Base 4 — Upper bound on s

There is no (135, 250, 3094)-net in base 4, because

1 times m-reduction [i] would yield (135, 249, 3094)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 829731 775679 134148 234724 574183 175161 657130 851321 735017 977985 004682 809872 406698 027356 771118 903216 789743 720636 120576 160464 374586 407947 217311 425420 560000 > 4²⁴⁹ [i]