MinT - Best Known (88−29, 88, s)-Nets in Base 5

Best Known (88−29, 88, s)-Nets in Base 5

(88−29, 88, 252)-Net over F₅ — Constructive and digital

Digital (59, 88, 252)-net over F₅, using

10 times m-reduction [i] based on digital (59, 98, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 49, 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]

(88−29, 88, 458)-Net over F₅ — Digital

Digital (59, 88, 458)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−29, 88, 33332)-Net in Base 5 — Upper bound on s

There is no (59, 88, 33333)-net in base 5, because

1 times m-reduction [i] would yield (59, 87, 33333)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 463931 426151 546583 816592 691073 148922 772918 616858 508000 856425 > 5⁸⁷ [i]