MinT - Best Known (81, 81+67, s)-Nets in Base 5

Best Known (81, 81+67, s)-Nets in Base 5

(81, 81+67, 132)-Net over F₅ — Constructive and digital

Digital (81, 148, 132)-net over F₅, using

t-expansion [i] based on digital (79, 148, 132)-net over F₅, using
- 2 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
  - trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
    - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
        a function field by GarcÃa and Quoos [i]

(81, 81+67, 202)-Net over F₅ — Digital

Digital (81, 148, 202)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+67, 4250)-Net in Base 5 — Upper bound on s

There is no (81, 148, 4251)-net in base 5, because

1 times m-reduction [i] would yield (81, 147, 4251)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 634554 496057 554091 511074 712111 273106 390611 702703 094400 087944 817348 740807 511794 514282 606892 285674 822125 > 5¹⁴⁷ [i]