MinT - Best Known (73, 73+74, s)-Nets in Base 5

Best Known (73, 73+74, s)-Nets in Base 5

(73, 73+74, 92)-Net over F₅ — Constructive and digital

Digital (73, 147, 92)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (5, 42, 20)-net over F₅, using
  - net from sequence [i] based on digital (5, 19)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 5 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 105, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(73, 73+74, 140)-Net over F₅ — Digital

Digital (73, 147, 140)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+74, 2164)-Net in Base 5 — Upper bound on s

There is no (73, 147, 2165)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 617391 394146 960977 144089 332937 631302 336727 024064 636663 446153 099940 017624 185285 465263 599448 378375 599749 > 5¹⁴⁷ [i]