MinT - Best Known (131, 246, s)-Nets in Base 4

Best Known (131, 246, s)-Nets in Base 4

(131, 246, 130)-Net over F₄ — Constructive and digital

Digital (131, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 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]

(131, 246, 214)-Net over F₄ — Digital

Digital (131, 246, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 246, 2802)-Net in Base 4 — Upper bound on s

There is no (131, 246, 2803)-net in base 4, because

1 times m-reduction [i] would yield (131, 245, 2803)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3249 174935 218995 529238 941181 651744 931267 092060 586041 640835 038537 270671 664325 611678 940608 460301 527437 865918 537819 055913 859715 090408 330963 529301 992016 > 4²⁴⁵ [i]