MinT - Best Known (87−30, 87, s)-Nets in Base 5

Best Known (87−30, 87, s)-Nets in Base 5

(87−30, 87, 252)-Net over F₅ — Constructive and digital

Digital (57, 87, 252)-net over F₅, using

7 times m-reduction [i] based on digital (57, 94, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 47, 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]

(87−30, 87, 379)-Net over F₅ — Digital

Digital (57, 87, 379)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−30, 87, 18175)-Net in Base 5 — Upper bound on s

There is no (57, 87, 18176)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 467342 820254 695389 713782 666552 876918 631111 599412 873317 653505 > 5⁸⁷ [i]