MinT - Best Known (63, 63+33, s)-Nets in Base 5

Best Known (63, 63+33, s)-Nets in Base 5

(63, 63+33, 252)-Net over F₅ — Constructive and digital

Digital (63, 96, 252)-net over F₅, using

10 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+33, 411)-Net over F₅ — Digital

Digital (63, 96, 411)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+33, 24010)-Net in Base 5 — Upper bound on s

There is no (63, 96, 24011)-net in base 5, because

1 times m-reduction [i] would yield (63, 95, 24011)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 524822 902524 324188 601288 897746 187957 276490 870628 849099 322340 914625 > 5⁹⁵ [i]