MinT - Best Known (78, 78+53, s)-Nets in Base 5

Best Known (78, 78+53, s)-Nets in Base 5

(78, 78+53, 252)-Net over F₅ — Constructive and digital

Digital (78, 131, 252)-net over F₅, using

5 times m-reduction [i] based on digital (78, 136, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 68, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(78, 78+53, 274)-Net over F₅ — Digital

Digital (78, 131, 274)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+53, 8223)-Net in Base 5 — Upper bound on s

There is no (78, 131, 8224)-net in base 5, because

1 times m-reduction [i] would yield (78, 130, 8224)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 347456 376262 443905 272159 360664 937801 233274 227746 687825 730265 719912 140538 706995 639163 806209 > 5¹³⁰ [i]