MinT - Best Known (78, 78+57, s)-Nets in Base 5

Best Known (78, 78+57, s)-Nets in Base 5

(78, 78+57, 252)-Net over F₅ — Constructive and digital

Digital (78, 135, 252)-net over F₅, using

1 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+57, 6231)-Net in Base 5 — Upper bound on s

There is no (78, 135, 6232)-net in base 5, because

1 times m-reduction [i] would yield (78, 134, 6232)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4602 520491 333098 744146 155491 869481 115783 273542 094296 792062 584094 799247 770070 202447 711960 443905 > 5¹³⁴ [i]