MinT - Best Known (130−33, 130, s)-Nets in Base 5

Best Known (130−33, 130, s)-Nets in Base 5

(130−33, 130, 408)-Net over F₅ — Constructive and digital

Digital (97, 130, 408)-net over F₅, using

4 times m-reduction [i] based on digital (97, 134, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 67, 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]

(130−33, 130, 2226)-Net over F₅ — Digital

Digital (97, 130, 2226)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−33, 130, 734374)-Net in Base 5 — Upper bound on s

There is no (97, 130, 734375)-net in base 5, because

1 times m-reduction [i] would yield (97, 129, 734375)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469383 717677 667950 855001 181802 717359 917726 203073 911195 387816 374047 717319 388641 284189 400001 > 5¹²⁹ [i]