MinT - Best Known (127−39, 127, s)-Nets in Base 5

Best Known (127−39, 127, s)-Nets in Base 5

(127−39, 127, 296)-Net over F₅ — Constructive and digital

Digital (88, 127, 296)-net over F₅, using

11 times m-reduction [i] based on digital (88, 138, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 69, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(127−39, 127, 833)-Net over F₅ — Digital

Digital (88, 127, 833)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−39, 127, 85577)-Net in Base 5 — Upper bound on s

There is no (88, 127, 85578)-net in base 5, because

1 times m-reduction [i] would yield (88, 126, 85578)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11755 777322 167878 068849 328589 579981 662601 531163 421546 825982 256385 728959 851676 756555 150025 > 5¹²⁶ [i]