MinT - Best Known (21−11, 21, s)-Nets in Base 5

Best Known (21−11, 21, s)-Nets in Base 5

(21−11, 21, 32)-Net over F₅ — Constructive and digital

Digital (10, 21, 32)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (2, 7, 21)-net over F₅, using
  - linear code embedding found in a computer search [i]
2. digital (3, 14, 16)-net over F₅, using
  - net from sequence [i] based on digital (3, 15)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]

(21−11, 21, 33)-Net over F₅ — Digital

Digital (10, 21, 33)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(21−11, 21, 403)-Net in Base 5 — Upper bound on s

There is no (10, 21, 404)-net in base 5, because

1 times m-reduction [i] would yield (10, 20, 404)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 95 580723 976145 > 5²⁰ [i]