MinT - Best Known (111−40, 111, s)-Nets in Base 5

Best Known (111−40, 111, s)-Nets in Base 5

(111−40, 111, 252)-Net over F₅ — Constructive and digital

Digital (71, 111, 252)-net over F₅, using

11 times m-reduction [i] based on digital (71, 122, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 61, 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]

(111−40, 111, 374)-Net over F₅ — Digital

Digital (71, 111, 374)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−40, 111, 15708)-Net in Base 5 — Upper bound on s

There is no (71, 111, 15709)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385528 990267 678711 862167 487242 084910 710855 833295 772662 650817 900849 539979 303345 > 5¹¹¹ [i]