MinT - Best Known (116−45, 116, s)-Nets in Base 5

Best Known (116−45, 116, s)-Nets in Base 5

(116−45, 116, 252)-Net over F₅ — Constructive and digital

Digital (71, 116, 252)-net over F₅, using

6 times m-reduction [i] based on digital (71, 122, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 61, 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]

(116−45, 116, 289)-Net over F₅ — Digital

Digital (71, 116, 289)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−45, 116, 10181)-Net in Base 5 — Upper bound on s

There is no (71, 116, 10182)-net in base 5, because

1 times m-reduction [i] would yield (71, 115, 10182)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 240 921140 459408 395836 365645 616568 372439 547620 758219 955656 097908 664733 411526 076225 > 5¹¹⁵ [i]