MinT - Best Known (77, 77+53, s)-Nets in Base 5

Best Known (77, 77+53, s)-Nets in Base 5

(77, 77+53, 252)-Net over F₅ — Constructive and digital

Digital (77, 130, 252)-net over F₅, using

4 times m-reduction [i] based on digital (77, 134, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 67, 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]

(77, 77+53, 264)-Net over F₅ — Digital

Digital (77, 130, 264)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+53, 7729)-Net in Base 5 — Upper bound on s

There is no (77, 130, 7730)-net in base 5, because

1 times m-reduction [i] would yield (77, 129, 7730)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 473342 012664 968986 127210 273555 126366 372833 384888 928244 227753 899830 522012 729512 019373 268161 > 5¹²⁹ [i]