MinT - Best Known (6, 48, s)-Nets in Base 49

Best Known (6, 48, s)-Nets in Base 49

(6, 48, 56)-Net over F₄₉ — Constructive and digital

Digital (6, 48, 56)-net over F₄₉, using

net from sequence [i] based on digital (6, 55)-sequence over F₄₉, using
- Niederreiter sequence [i]

(6, 48, 92)-Net over F₄₉ — Digital

Digital (6, 48, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 48, 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]

(6, 48, 1309)-Net in Base 49 — Upper bound on s

There is no (6, 48, 1310)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 1357 306003 506726 739261 375145 427268 446496 272725 233230 947142 701006 439569 663691 728929 > 49⁴⁸ [i]