MinT - Best Known (100, 145, s)-Nets in Base 5

Best Known (100, 145, s)-Nets in Base 5

(100, 145, 400)-Net over F₅ — Constructive and digital

Digital (100, 145, 400)-net over F₅, using

5 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 75, 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]

(100, 145, 889)-Net over F₅ — Digital

Digital (100, 145, 889)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 145, 85072)-Net in Base 5 — Upper bound on s

There is no (100, 145, 85073)-net in base 5, because

1 times m-reduction [i] would yield (100, 144, 85073)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44850 607303 596597 533214 228223 615540 836506 374108 751067 497337 157036 099864 489459 334451 023417 557854 789321 > 5¹⁴⁴ [i]