MinT - Best Known (62, 62+31, s)-Nets in Base 5

Best Known (62, 62+31, s)-Nets in Base 5

(62, 62+31, 252)-Net over F₅ — Constructive and digital

Digital (62, 93, 252)-net over F₅, using

11 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]

(62, 62+31, 457)-Net over F₅ — Digital

Digital (62, 93, 457)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+31, 31086)-Net in Base 5 — Upper bound on s

There is no (62, 93, 31087)-net in base 5, because

1 times m-reduction [i] would yield (62, 92, 31087)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20199 215054 690245 843281 137495 774771 946289 333817 705284 826610 547845 > 5⁹² [i]