MinT - Best Known (75, 75+43, s)-Nets in Base 5

Best Known (75, 75+43, s)-Nets in Base 5

(75, 75+43, 252)-Net over F₅ — Constructive and digital

Digital (75, 118, 252)-net over F₅, using

12 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+43, 374)-Net over F₅ — Digital

Digital (75, 118, 374)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+43, 16994)-Net in Base 5 — Upper bound on s

There is no (75, 118, 16995)-net in base 5, because

1 times m-reduction [i] would yield (75, 117, 16995)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6023 347058 774058 078405 525082 876962 022800 224091 272396 755810 749130 516288 635300 467005 > 5¹¹⁷ [i]