MinT - Best Known (80, 80+22, s)-Nets in Base 5

Best Known (80, 80+22, s)-Nets in Base 5

(80, 80+22, 424)-Net over F₅ — Constructive and digital

Digital (80, 102, 424)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (27, 38, 172)-net over F₅, using
  - (u,Â u+v)-construction [i] based on
    1. digital (5, 10, 68)-net over F₅, using
      - linear code embedding found in a computer search [i]
    2. digital (17, 28, 104)-net over F₅, using
      - trace code for nets [i] based on digital (3, 14, 52)-net over F₂₅, using
        net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
        a function field by GarcÃa and Quoos [i]
2. digital (42, 64, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 32, 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]

(80, 80+22, 5398)-Net over F₅ — Digital

Digital (80, 102, 5398)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+22, 3718017)-Net in Base 5 — Upper bound on s

There is no (80, 102, 3718018)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197215 258099 495011 586221 553636 008382 888869 438066 852817 673924 013378 502569 > 5¹⁰² [i]