MinT - Best Known (142−63, 142, s)-Nets in Base 5

Best Known (142−63, 142, s)-Nets in Base 5

(142−63, 142, 132)-Net over F₅ — Constructive and digital

Digital (79, 142, 132)-net over F₅, using

8 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(142−63, 142, 210)-Net over F₅ — Digital

Digital (79, 142, 210)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−63, 142, 4667)-Net in Base 5 — Upper bound on s

There is no (79, 142, 4668)-net in base 5, because

1 times m-reduction [i] would yield (79, 141, 4668)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 360 774431 733211 916493 994463 699516 843648 396511 269397 531334 649264 304453 175208 679725 757977 751304 036209 > 5¹⁴¹ [i]