MinT - Best Known (64, 64+33, s)-Nets in Base 5

Best Known (64, 64+33, s)-Nets in Base 5

(64, 64+33, 252)-Net over F₅ — Constructive and digital

Digital (64, 97, 252)-net over F₅, using

11 times m-reduction [i] based on digital (64, 108, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 54, 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]

(64, 64+33, 434)-Net over F₅ — Digital

Digital (64, 97, 434)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+33, 26552)-Net in Base 5 — Upper bound on s

There is no (64, 97, 26553)-net in base 5, because

1 times m-reduction [i] would yield (64, 96, 26553)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 623103 101620 948758 078585 116908 835914 766312 480984 406424 049914 211265 > 5⁹⁶ [i]