MinT - Best Known (172−67, 172, s)-Nets in Base 4

Best Known (172−67, 172, s)-Nets in Base 4

(172−67, 172, 130)-Net over F₄ — Constructive and digital

Digital (105, 172, 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]

(172−67, 172, 280)-Net over F₄ — Digital

Digital (105, 172, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−67, 172, 5753)-Net in Base 4 — Upper bound on s

There is no (105, 172, 5754)-net in base 4, because

1 times m-reduction [i] would yield (105, 171, 5754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 959709 540929 821493 083382 256658 188675 291698 773812 311711 131452 998158 314338 089276 892495 411058 012799 398947 > 4¹⁷¹ [i]