MinT - Best Known (126−45, 126, s)-Nets in Base 5

Best Known (126−45, 126, s)-Nets in Base 5

(126−45, 126, 252)-Net over F₅ — Constructive and digital

Digital (81, 126, 252)-net over F₅, using

16 times m-reduction [i] based on digital (81, 142, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 71, 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]

(126−45, 126, 429)-Net over F₅ — Digital

Digital (81, 126, 429)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−45, 126, 21178)-Net in Base 5 — Upper bound on s

There is no (81, 126, 21179)-net in base 5, because

1 times m-reduction [i] would yield (81, 125, 21179)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2353 349956 505646 178419 236703 473909 627358 047198 029729 676130 487299 276801 109302 582450 004905 > 5¹²⁵ [i]