MinT - Best Known (78, 78+66, s)-Nets in Base 5

Best Known (78, 78+66, s)-Nets in Base 5

(78, 78+66, 132)-Net over F₅ — Constructive and digital

Digital (78, 144, 132)-net over F₅, using

4 times m-reduction [i] based on digital (78, 148, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 74, 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]

(78, 78+66, 189)-Net over F₅ — Digital

Digital (78, 144, 189)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+66, 3668)-Net in Base 5 — Upper bound on s

There is no (78, 144, 3669)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45036 129698 736038 574958 945090 742239 411559 672950 438641 488960 616213 777399 903995 927424 646841 157613 786837 > 5¹⁴⁴ [i]