MinT - Best Known (141−57, 141, s)-Nets in Base 5

Best Known (141−57, 141, s)-Nets in Base 5

(141−57, 141, 252)-Net over F₅ — Constructive and digital

Digital (84, 141, 252)-net over F₅, using

7 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 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]

(141−57, 141, 292)-Net over F₅ — Digital

Digital (84, 141, 292)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−57, 141, 8806)-Net in Base 5 — Upper bound on s

There is no (84, 141, 8807)-net in base 5, because

1 times m-reduction [i] would yield (84, 140, 8807)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 940221 685670 299124 836576 341209 100543 440765 370732 204458 838841 804475 870014 423474 660514 272030 379665 > 5¹⁴⁰ [i]