MinT - Best Known (149−55, 149, s)-Nets in Base 5

Best Known (149−55, 149, s)-Nets in Base 5

(149−55, 149, 296)-Net over F₅ — Constructive and digital

Digital (94, 149, 296)-net over F₅, using

1 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(149−55, 149, 430)-Net over F₅ — Digital

Digital (94, 149, 430)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−55, 149, 18504)-Net in Base 5 — Upper bound on s

There is no (94, 149, 18505)-net in base 5, because

1 times m-reduction [i] would yield (94, 148, 18505)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 050835 186682 448529 474648 997354 962969 035273 770841 800277 156897 263622 615938 013854 230367 827322 603342 042685 > 5¹⁴⁸ [i]