MinT - Best Known (144−55, 144, s)-Nets in Base 5

Best Known (144−55, 144, s)-Nets in Base 5

(144−55, 144, 252)-Net over F₅ — Constructive and digital

Digital (89, 144, 252)-net over F₅, using

t-expansion [i] based on digital (85, 144, 252)-net over F₅, using
- 6 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]

(144−55, 144, 366)-Net over F₅ — Digital

Digital (89, 144, 366)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−55, 144, 13730)-Net in Base 5 — Upper bound on s

There is no (89, 144, 13731)-net in base 5, because

1 times m-reduction [i] would yield (89, 143, 13731)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8983 399799 596102 837064 436673 446575 737496 216242 704613 804048 489534 547450 614772 166131 068388 788850 522085 > 5¹⁴³ [i]