MinT - Best Known (130, 130+125, s)-Nets in Base 4

Best Known (130, 130+125, s)-Nets in Base 4

(130, 130+125, 130)-Net over F₄ — Constructive and digital

Digital (130, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(130, 130+125, 190)-Net over F₄ — Digital

Digital (130, 255, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+125, 2284)-Net in Base 4 — Upper bound on s

There is no (130, 255, 2285)-net in base 4, because

1 times m-reduction [i] would yield (130, 254, 2285)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 843 293214 612719 652230 747853 185959 407572 064873 451902 453760 340841 082202 460145 886348 267870 723469 169454 397243 135990 767121 470839 501326 957672 306254 409644 627680 > 4²⁵⁴ [i]