MinT - Best Known (63, 63+37, s)-Nets in Base 5

Best Known (63, 63+37, s)-Nets in Base 5

(63, 63+37, 252)-Net over F₅ — Constructive and digital

Digital (63, 100, 252)-net over F₅, using

6 times m-reduction [i] based on digital (63, 106, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 53, 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]

(63, 63+37, 309)-Net over F₅ — Digital

Digital (63, 100, 309)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+37, 13181)-Net in Base 5 — Upper bound on s

There is no (63, 100, 13182)-net in base 5, because

1 times m-reduction [i] would yield (63, 99, 13182)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1577 993376 433581 726676 323441 440922 320209 934850 435960 403419 370750 497025 > 5⁹⁹ [i]