MinT - Best Known (82−29, 82, s)-Nets in Base 5

Best Known (82−29, 82, s)-Nets in Base 5

(82−29, 82, 252)-Net over F₅ — Constructive and digital

Digital (53, 82, 252)-net over F₅, using

4 times m-reduction [i] based on digital (53, 86, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 43, 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]

(82−29, 82, 325)-Net over F₅ — Digital

Digital (53, 82, 325)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−29, 82, 16717)-Net in Base 5 — Upper bound on s

There is no (53, 82, 16718)-net in base 5, because

1 times m-reduction [i] would yield (53, 81, 16718)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 413 663316 597105 181158 999876 145123 960071 684749 948350 013505 > 5⁸¹ [i]