MinT - Best Known (48, 73, s)-Nets in Base 5

Best Known (48, 73, s)-Nets in Base 5

(48, 73, 252)-Net over F₅ — Constructive and digital

Digital (48, 73, 252)-net over F₅, using

3 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, 73, 339)-Net over F₅ — Digital

Digital (48, 73, 339)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 73, 20651)-Net in Base 5 — Upper bound on s

There is no (48, 73, 20652)-net in base 5, because

1 times m-reduction [i] would yield (48, 72, 20652)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 211 871498 492979 339592 329100 823106 664089 128880 276225 > 5⁷² [i]