MinT - Best Known (48, 75, s)-Nets in Base 5

Best Known (48, 75, s)-Nets in Base 5

(48, 75, 252)-Net over F₅ — Constructive and digital

Digital (48, 75, 252)-net over F₅, using

1 times m-reduction [i] based on digital (48, 76, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 38, 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]

(48, 75, 283)-Net over F₅ — Digital

Digital (48, 75, 283)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 75, 13483)-Net in Base 5 — Upper bound on s

There is no (48, 75, 13484)-net in base 5, because

1 times m-reduction [i] would yield (48, 74, 13484)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5296 804802 000125 522542 137609 875960 783024 658901 679665 > 5⁷⁴ [i]