MinT - Best Known (82, 82+39, s)-Nets in Base 5

Best Known (82, 82+39, s)-Nets in Base 5

(82, 82+39, 296)-Net over F₅ — Constructive and digital

Digital (82, 121, 296)-net over F₅, using

5 times m-reduction [i] based on digital (82, 126, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 63, 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]

(82, 82+39, 650)-Net over F₅ — Digital

Digital (82, 121, 650)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+39, 51473)-Net in Base 5 — Upper bound on s

There is no (82, 121, 51474)-net in base 5, because

1 times m-reduction [i] would yield (82, 120, 51474)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 752349 022877 215940 761948 960313 537060 533897 419558 084880 129746 838192 128349 434980 750825 > 5¹²⁰ [i]