MinT - Best Known (81, 81+52, s)-Nets in Base 5

Best Known (81, 81+52, s)-Nets in Base 5

(81, 81+52, 252)-Net over F₅ — Constructive and digital

Digital (81, 133, 252)-net over F₅, using

9 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]

(81, 81+52, 314)-Net over F₅ — Digital

Digital (81, 133, 314)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+52, 9906)-Net in Base 5 — Upper bound on s

There is no (81, 133, 9907)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 920 570261 414096 812839 978469 288113 199853 092652 649095 398242 638194 112154 457890 035706 187661 373721 > 5¹³³ [i]