MinT - Best Known (82, 82+63, s)-Nets in Base 5

Best Known (82, 82+63, s)-Nets in Base 5

(82, 82+63, 208)-Net over F₅ — Constructive and digital

Digital (82, 145, 208)-net over F₅, using

1 times m-reduction [i] based on digital (82, 146, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 73, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(82, 82+63, 230)-Net over F₅ — Digital

Digital (82, 145, 230)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+63, 5457)-Net in Base 5 — Upper bound on s

There is no (82, 145, 5458)-net in base 5, because

1 times m-reduction [i] would yield (82, 144, 5458)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44956 743581 036093 297368 422647 617847 192465 471897 178870 752229 751710 239540 812335 403914 654697 324485 698409 > 5¹⁴⁴ [i]