MinT - Best Known (38, 38+18, s)-Nets in Base 5

Best Known (38, 38+18, s)-Nets in Base 5

(38, 38+18, 252)-Net over F₅ — Constructive and digital

Digital (38, 56, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 28, 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]

(38, 38+18, 368)-Net over F₅ — Digital

Digital (38, 56, 368)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+18, 23159)-Net in Base 5 — Upper bound on s

There is no (38, 56, 23160)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1388 284361 779803 906017 471737 979078 681569 > 5⁵⁶ [i]