MinT - Best Known (72, 72+43, s)-Nets in Base 5

Best Known (72, 72+43, s)-Nets in Base 5

(72, 72+43, 252)-Net over F₅ — Constructive and digital

Digital (72, 115, 252)-net over F₅, using

9 times m-reduction [i] based on digital (72, 124, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 62, 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]

(72, 72+43, 331)-Net over F₅ — Digital

Digital (72, 115, 331)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+43, 13500)-Net in Base 5 — Upper bound on s

There is no (72, 115, 13501)-net in base 5, because

1 times m-reduction [i] would yield (72, 114, 13501)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 182824 302824 695070 516821 747824 865736 765776 177658 871125 126097 050885 761577 553125 > 5¹¹⁴ [i]