MinT - Best Known (120−43, 120, s)-Nets in Base 5

Best Known (120−43, 120, s)-Nets in Base 5

(120−43, 120, 252)-Net over F₅ — Constructive and digital

Digital (77, 120, 252)-net over F₅, using

14 times m-reduction [i] based on digital (77, 134, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 67, 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]

(120−43, 120, 407)-Net over F₅ — Digital

Digital (77, 120, 407)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−43, 120, 19812)-Net in Base 5 — Upper bound on s

There is no (77, 120, 19813)-net in base 5, because

1 times m-reduction [i] would yield (77, 119, 19813)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150621 186647 333148 025933 775888 640247 540191 491542 282579 197598 590081 961733 102465 015685 > 5¹¹⁹ [i]