MinT - Best Known (78, 78+69, s)-Nets in Base 5

Best Known (78, 78+69, s)-Nets in Base 5

(78, 78+69, 132)-Net over F₅ — Constructive and digital

Digital (78, 147, 132)-net over F₅, using

1 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+69, 178)-Net over F₅ — Digital

Digital (78, 147, 178)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+69, 3370)-Net in Base 5 — Upper bound on s

There is no (78, 147, 3371)-net in base 5, because

1 times m-reduction [i] would yield (78, 146, 3371)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 128473 172970 101221 105876 772478 677429 422405 064372 760084 965550 915116 266100 588183 501662 261299 093940 150265 > 5¹⁴⁶ [i]