MinT - Best Known (145−41, 145, s)-Nets in Base 5

Best Known (145−41, 145, s)-Nets in Base 5

(145−41, 145, 408)-Net over F₅ — Constructive and digital

Digital (104, 145, 408)-net over F₅, using

3 times m-reduction [i] based on digital (104, 148, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 74, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(145−41, 145, 1367)-Net over F₅ — Digital

Digital (104, 145, 1367)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−41, 145, 223770)-Net in Base 5 — Upper bound on s

There is no (104, 145, 223771)-net in base 5, because

1 times m-reduction [i] would yield (104, 144, 223771)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44845 003619 532041 144061 855527 245611 358713 600352 350399 530502 342703 155168 251598 197023 683360 647274 596401 > 5¹⁴⁴ [i]