MinT - Best Known (82, 82+67, s)-Nets in Base 5

Best Known (82, 82+67, s)-Nets in Base 5

(82, 82+67, 132)-Net over F₅ — Constructive and digital

Digital (82, 149, 132)-net over F₅, using

t-expansion [i] based on digital (79, 149, 132)-net over F₅, using
- 1 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]

(82, 82+67, 208)-Net over F₅ — Digital

Digital (82, 149, 208)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+67, 4463)-Net in Base 5 — Upper bound on s

There is no (82, 149, 4464)-net in base 5, because

1 times m-reduction [i] would yield (82, 148, 4464)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 034130 569923 578017 724771 232505 077508 755464 864207 809418 693452 517083 253561 391529 889528 848686 943267 067329 > 5¹⁴⁸ [i]