MinT - Best Known (130−35, 130, s)-Nets in Base 5

Best Known (130−35, 130, s)-Nets in Base 5

(130−35, 130, 408)-Net over F₅ — Constructive and digital

Digital (95, 130, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 65, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(130−35, 130, 1609)-Net over F₅ — Digital

Digital (95, 130, 1609)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−35, 130, 361259)-Net in Base 5 — Upper bound on s

There is no (95, 130, 361260)-net in base 5, because

1 times m-reduction [i] would yield (95, 129, 361260)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469398 527167 616263 614158 915903 288285 059806 860533 570897 330404 634088 591792 884932 968192 936625 > 5¹²⁹ [i]