MinT - Best Known (14, 14+15, s)-Nets in Base 5

Best Known (14, 14+15, s)-Nets in Base 5

(14, 14+15, 36)-Net over F₅ — Constructive and digital

Digital (14, 29, 36)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (3, 10, 25)-net over F₅, using
  - linear code embedding found in a computer search [i]
2. digital (4, 19, 18)-net over F₅, using
  - net from sequence [i] based on digital (4, 17)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
      - an explicitly constructive algebraic function field [i]

(14, 14+15, 40)-Net over F₅ — Digital

Digital (14, 29, 40)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(14, 14+15, 523)-Net in Base 5 — Upper bound on s

There is no (14, 29, 524)-net in base 5, because

1 times m-reduction [i] would yield (14, 28, 524)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 37 553402 284290 752433 > 5²⁸ [i]