MinT - Best Known (47, 47+27, s)-Nets in Base 5

Best Known (47, 47+27, s)-Nets in Base 5

(47, 47+27, 252)-Net over F₅ — Constructive and digital

Digital (47, 74, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 37, 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]

(47, 47+27, 265)-Net over F₅ — Digital

Digital (47, 74, 265)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+27, 11912)-Net in Base 5 — Upper bound on s

There is no (47, 74, 11913)-net in base 5, because

1 times m-reduction [i] would yield (47, 73, 11913)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1059 632432 063945 307636 088323 757666 356928 401127 011765 > 5⁷³ [i]