MinT - Best Known (120−44, 120, s)-Nets in Base 5

Best Known (120−44, 120, s)-Nets in Base 5

(120−44, 120, 252)-Net over F₅ — Constructive and digital

Digital (76, 120, 252)-net over F₅, using

12 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(120−44, 120, 370)-Net over F₅ — Digital

Digital (76, 120, 370)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−44, 120, 14685)-Net in Base 5 — Upper bound on s

There is no (76, 120, 14686)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 753061 324026 241183 419063 803882 265434 851237 312353 665719 901302 202221 807112 693371 148225 > 5¹²⁰ [i]