MinT - Best Known (117−41, 117, s)-Nets in Base 5

Best Known (117−41, 117, s)-Nets in Base 5

(117−41, 117, 252)-Net over F₅ — Constructive and digital

Digital (76, 117, 252)-net over F₅, using

15 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(117−41, 117, 438)-Net over F₅ — Digital

Digital (76, 117, 438)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−41, 117, 23496)-Net in Base 5 — Upper bound on s

There is no (76, 117, 23497)-net in base 5, because

1 times m-reduction [i] would yield (76, 116, 23497)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1204 150480 622955 027770 030848 217123 985684 049370 594106 938820 620198 988234 711230 575921 > 5¹¹⁶ [i]