MinT - Best Known (147−61, 147, s)-Nets in Base 5

Best Known (147−61, 147, s)-Nets in Base 5

(147−61, 147, 252)-Net over F₅ — Constructive and digital

Digital (86, 147, 252)-net over F₅, using

t-expansion [i] based on digital (85, 147, 252)-net over F₅, using
- 3 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(147−61, 147, 275)-Net over F₅ — Digital

Digital (86, 147, 275)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−61, 147, 7570)-Net in Base 5 — Upper bound on s

There is no (86, 147, 7571)-net in base 5, because

1 times m-reduction [i] would yield (86, 146, 7571)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 123317 520789 775116 652490 888729 757643 627810 487859 596986 288564 758134 450755 602830 503053 691683 447075 791753 > 5¹⁴⁶ [i]