MinT - Best Known (149−49, 149, s)-Nets in Base 5

Best Known (149−49, 149, s)-Nets in Base 5

(149−49, 149, 400)-Net over F₅ — Constructive and digital

Digital (100, 149, 400)-net over F₅, using

1 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]

(149−49, 149, 700)-Net over F₅ — Digital

Digital (100, 149, 700)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−49, 149, 50057)-Net in Base 5 — Upper bound on s

There is no (100, 149, 50058)-net in base 5, because

1 times m-reduction [i] would yield (100, 148, 50058)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 037593 114219 164505 276458 116998 130610 973205 917837 145297 325913 764499 693303 966484 144666 603654 072342 980225 > 5¹⁴⁸ [i]