MinT - Best Known (131−41, 131, s)-Nets in Base 5

Best Known (131−41, 131, s)-Nets in Base 5

(131−41, 131, 296)-Net over F₅ — Constructive and digital

Digital (90, 131, 296)-net over F₅, using

11 times m-reduction [i] based on digital (90, 142, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 71, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(131−41, 131, 787)-Net over F₅ — Digital

Digital (90, 131, 787)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−41, 131, 72521)-Net in Base 5 — Upper bound on s

There is no (90, 131, 72522)-net in base 5, because

1 times m-reduction [i] would yield (90, 130, 72522)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 348640 660280 119678 033711 987504 228055 152154 903626 410605 371378 504857 808316 188705 881109 977921 > 5¹³⁰ [i]