MinT - Best Known (131−47, 131, s)-Nets in Base 5

Best Known (131−47, 131, s)-Nets in Base 5

(131−47, 131, 252)-Net over F₅ — Constructive and digital

Digital (84, 131, 252)-net over F₅, using

17 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(131−47, 131, 434)-Net over F₅ — Digital

Digital (84, 131, 434)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−47, 131, 21025)-Net in Base 5 — Upper bound on s

There is no (84, 131, 21026)-net in base 5, because

1 times m-reduction [i] would yield (84, 130, 21026)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 349207 181832 028474 108021 341191 451073 031992 813791 584927 070720 797776 323084 106540 992572 934825 > 5¹³⁰ [i]