MinT - Best Known (101−37, 101, s)-Nets in Base 5

Best Known (101−37, 101, s)-Nets in Base 5

(101−37, 101, 252)-Net over F₅ — Constructive and digital

Digital (64, 101, 252)-net over F₅, using

7 times m-reduction [i] based on digital (64, 108, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 54, 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]

(101−37, 101, 325)-Net over F₅ — Digital

Digital (64, 101, 325)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−37, 101, 14416)-Net in Base 5 — Upper bound on s

There is no (64, 101, 14417)-net in base 5, because

1 times m-reduction [i] would yield (64, 100, 14417)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7898 242869 006303 667216 884763 113284 575467 568341 750306 747835 386958 910425 > 5¹⁰⁰ [i]