MinT - Best Known (75, 75+49, s)-Nets in Base 5

Best Known (75, 75+49, s)-Nets in Base 5

(75, 75+49, 252)-Net over F₅ — Constructive and digital

Digital (75, 124, 252)-net over F₅, using

6 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 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]

(75, 75+49, 285)-Net over F₅ — Digital

Digital (75, 124, 285)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+49, 9347)-Net in Base 5 — Upper bound on s

There is no (75, 124, 9348)-net in base 5, because

1 times m-reduction [i] would yield (75, 123, 9348)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 072844 085121 812176 428103 519727 746675 999871 404798 301551 597927 101408 267304 967952 743425 > 5¹²³ [i]