MinT - Best Known (99−37, 99, s)-Nets in Base 5

Best Known (99−37, 99, s)-Nets in Base 5

(99−37, 99, 252)-Net over F₅ — Constructive and digital

Digital (62, 99, 252)-net over F₅, using

5 times m-reduction [i] based on digital (62, 104, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 52, 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]

(99−37, 99, 295)-Net over F₅ — Digital

Digital (62, 99, 295)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−37, 99, 12053)-Net in Base 5 — Upper bound on s

There is no (62, 99, 12054)-net in base 5, because

1 times m-reduction [i] would yield (62, 98, 12054)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 880753 400607 625242 953225 338334 201719 259257 226659 781534 125925 724545 > 5⁹⁸ [i]