MinT - Best Known (82, 82+65, s)-Nets in Base 5

Best Known (82, 82+65, s)-Nets in Base 5

(82, 82+65, 132)-Net over F₅ — Constructive and digital

Digital (82, 147, 132)-net over F₅, using

t-expansion [i] based on digital (79, 147, 132)-net over F₅, using
- 3 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+65, 218)-Net over F₅ — Digital

Digital (82, 147, 218)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+65, 4918)-Net in Base 5 — Upper bound on s

There is no (82, 147, 4919)-net in base 5, because

1 times m-reduction [i] would yield (82, 146, 4919)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 127014 505837 787157 725230 693358 432596 033889 377593 904745 862837 485574 582819 681719 971289 713264 515011 659649 > 5¹⁴⁶ [i]