MinT - Best Known (101−39, 101, s)-Nets in Base 5

Best Known (101−39, 101, s)-Nets in Base 5

(101−39, 101, 252)-Net over F₅ — Constructive and digital

Digital (62, 101, 252)-net over F₅, using

3 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]

(101−39, 101, 263)-Net over F₅ — Digital

Digital (62, 101, 263)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−39, 101, 9447)-Net in Base 5 — Upper bound on s

There is no (62, 101, 9448)-net in base 5, because

1 times m-reduction [i] would yield (62, 100, 9448)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7897 630643 892891 875243 467207 316544 200303 438591 071886 609838 891397 607585 > 5¹⁰⁰ [i]