MinT - Best Known (251−127, 251, s)-Nets in Base 4

Best Known (251−127, 251, s)-Nets in Base 4

(251−127, 251, 130)-Net over F₄ — Constructive and digital

Digital (124, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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]

(251−127, 251, 169)-Net over F₄ — Digital

Digital (124, 251, 169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−127, 251, 1933)-Net in Base 4 — Upper bound on s

There is no (124, 251, 1934)-net in base 4, because

1 times m-reduction [i] would yield (124, 250, 1934)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 365300 592214 105529 157342 887512 596932 283987 984185 071535 391347 486117 557862 654630 646348 028886 826843 385331 217926 956058 448089 446005 274737 222112 096708 914880 > 4²⁵⁰ [i]