MinT - Best Known (129−38, 129, s)-Nets in Base 5

Best Known (129−38, 129, s)-Nets in Base 5

(129−38, 129, 400)-Net over F₅ — Constructive and digital

Digital (91, 129, 400)-net over F₅, using

3 times m-reduction [i] based on digital (91, 132, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 66, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(129−38, 129, 1020)-Net over F₅ — Digital

Digital (91, 129, 1020)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−38, 129, 110341)-Net in Base 5 — Upper bound on s

There is no (91, 129, 110342)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469432 138453 695113 804327 052154 746200 293549 670332 726255 380719 848251 428994 573032 245512 148025 > 5¹²⁹ [i]