MinT - Best Known (14, 14+31, s)-Nets in Base 49

Best Known (14, 14+31, s)-Nets in Base 49

(14, 14+31, 64)-Net over F₄₉ — Constructive and digital

Digital (14, 45, 64)-net over F₄₉, using

net from sequence [i] based on digital (14, 63)-sequence over F₄₉, using
- Niederreiter sequence [i]

(14, 14+31, 92)-Net over F₄₉ — Digital

Digital (14, 45, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 45, 92)-net over F₄₉, using
- net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(14, 14+31, 12138)-Net in Base 49 — Upper bound on s

There is no (14, 45, 12139)-net in base 49, because

1 times m-reduction [i] would yield (14, 44, 12139)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 233 768072 276095 787171 424433 234350 209288 487056 357720 608730 645171 578196 012785 > 49⁴⁴ [i]