MinT - Best Known (116−41, 116, s)-Nets in Base 5

Best Known (116−41, 116, s)-Nets in Base 5

(116−41, 116, 252)-Net over F₅ — Constructive and digital

Digital (75, 116, 252)-net over F₅, using

14 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 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]

(116−41, 116, 419)-Net over F₅ — Digital

Digital (75, 116, 419)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−41, 116, 21678)-Net in Base 5 — Upper bound on s

There is no (75, 116, 21679)-net in base 5, because

1 times m-reduction [i] would yield (75, 115, 21679)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 240 805460 346226 791420 537913 717030 369294 710439 802435 802169 490024 133959 443631 895985 > 5¹¹⁵ [i]