MinT - Best Known (252−145, 252, s)-Nets in Base 4

Best Known (252−145, 252, s)-Nets in Base 4

(252−145, 252, 130)-Net over F₄ — Constructive and digital

Digital (107, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(252−145, 252, 144)-Net over F₄ — Digital

Digital (107, 252, 144)-net over F₄, using

t-expansion [i] based on digital (91, 252, 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]

(252−145, 252, 1098)-Net in Base 4 — Upper bound on s

There is no (107, 252, 1099)-net in base 4, because

1 times m-reduction [i] would yield (107, 251, 1099)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 663220 112182 948638 349962 510548 332429 549413 709175 550780 898615 298068 710989 892413 076723 806971 766955 408348 044022 649983 958715 978385 571954 468936 556127 786525 > 4²⁵¹ [i]