MinT - Best Known (84, 84+65, s)-Nets in Base 5

Best Known (84, 84+65, s)-Nets in Base 5

(84, 84+65, 208)-Net over F₅ — Constructive and digital

Digital (84, 149, 208)-net over F₅, using

1 times m-reduction [i] based on digital (84, 150, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 75, 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]

(84, 84+65, 232)-Net over F₅ — Digital

Digital (84, 149, 232)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+65, 5441)-Net in Base 5 — Upper bound on s

There is no (84, 149, 5442)-net in base 5, because

1 times m-reduction [i] would yield (84, 148, 5442)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 171695 498633 477158 025506 060704 165793 697218 159757 328157 048524 837739 046543 071588 736860 232543 301503 686145 > 5¹⁴⁸ [i]