MinT - Best Known (141−59, 141, s)-Nets in Base 5

Best Known (141−59, 141, s)-Nets in Base 5

(141−59, 141, 252)-Net over F₅ — Constructive and digital

Digital (82, 141, 252)-net over F₅, using

3 times m-reduction [i] based on digital (82, 144, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 72, 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]

(141−59, 141, 258)-Net over F₅ — Digital

Digital (82, 141, 258)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−59, 141, 6887)-Net in Base 5 — Upper bound on s

There is no (82, 141, 6888)-net in base 5, because

1 times m-reduction [i] would yield (82, 140, 6888)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 887701 058374 568226 088871 953360 301619 981894 407909 302336 299170 931780 796838 343090 510832 524363 902625 > 5¹⁴⁰ [i]