MinT - Best Known (141−43, 141, s)-Nets in Base 5

Best Known (141−43, 141, s)-Nets in Base 5

(141−43, 141, 400)-Net over F₅ — Constructive and digital

Digital (98, 141, 400)-net over F₅, using

5 times m-reduction [i] based on digital (98, 146, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 73, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(141−43, 141, 938)-Net over F₅ — Digital

Digital (98, 141, 938)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−43, 141, 99121)-Net in Base 5 — Upper bound on s

There is no (98, 141, 99122)-net in base 5, because

1 times m-reduction [i] would yield (98, 140, 99122)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 761259 103754 979682 286635 139284 678634 129277 485933 472296 012090 746139 745058 590900 516614 928352 331209 > 5¹⁴⁰ [i]