MinT - Best Known (89−30, 89, s)-Nets in Base 5

Best Known (89−30, 89, s)-Nets in Base 5

(89−30, 89, 252)-Net over F₅ — Constructive and digital

Digital (59, 89, 252)-net over F₅, using

9 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]

(89−30, 89, 422)-Net over F₅ — Digital

Digital (59, 89, 422)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−30, 89, 22527)-Net in Base 5 — Upper bound on s

There is no (59, 89, 22528)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 161 564936 506015 708271 922491 294606 087797 280664 406863 156349 067265 > 5⁸⁹ [i]