MinT - Best Known (127−51, 127, s)-Nets in Base 5

Best Known (127−51, 127, s)-Nets in Base 5

(127−51, 127, 252)-Net over F₅ — Constructive and digital

Digital (76, 127, 252)-net over F₅, using

5 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(127−51, 127, 274)-Net over F₅ — Digital

Digital (76, 127, 274)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−51, 127, 8461)-Net in Base 5 — Upper bound on s

There is no (76, 127, 8462)-net in base 5, because

1 times m-reduction [i] would yield (76, 126, 8462)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11777 481566 116904 274581 534789 845801 817628 748836 560597 590217 606297 743527 945683 108611 883577 > 5¹²⁶ [i]