MinT - Best Known (72, 145, s)-Nets in Base 5

Best Known (72, 145, s)-Nets in Base 5

(72, 145, 92)-Net over F₅ — Constructive and digital

Digital (72, 145, 92)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (5, 41, 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, 104, 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]

(72, 145, 138)-Net over F₅ — Digital

Digital (72, 145, 138)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 145, 2204)-Net in Base 5 — Upper bound on s

There is no (72, 145, 2205)-net in base 5, because

1 times m-reduction [i] would yield (72, 144, 2205)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44908 615903 582866 122671 519824 292543 248862 405079 210788 493411 256925 715889 991675 364636 362377 087971 882865 > 5¹⁴⁴ [i]