MinT - Best Known (82, 82+41, s)-Nets in Base 5

Best Known (82, 82+41, s)-Nets in Base 5

(82, 82+41, 296)-Net over F₅ — Constructive and digital

Digital (82, 123, 296)-net over F₅, using

3 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+41, 567)-Net over F₅ — Digital

Digital (82, 123, 567)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+41, 38088)-Net in Base 5 — Upper bound on s

There is no (82, 123, 38089)-net in base 5, because

1 times m-reduction [i] would yield (82, 122, 38089)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 18 809278 995612 155056 382051 337429 933288 752098 963687 887793 277852 480278 600455 006993 536305 > 5¹²² [i]