MinT - Best Known (80, 80+70, s)-Nets in Base 5

Best Known (80, 80+70, s)-Nets in Base 5

(80, 80+70, 132)-Net over F₅ — Constructive and digital

Digital (80, 150, 132)-net over F₅, using

t-expansion [i] based on digital (79, 150, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(80, 80+70, 184)-Net over F₅ — Digital

Digital (80, 150, 184)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+70, 3416)-Net in Base 5 — Upper bound on s

There is no (80, 150, 3417)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 706 734604 544767 027092 889794 128382 039393 659617 507949 574567 174534 218813 828513 368979 443827 425750 809638 177757 > 5¹⁵⁰ [i]