MinT - Best Known (12, 12+27, s)-Nets in Base 49

Best Known (12, 12+27, s)-Nets in Base 49

(12, 12+27, 62)-Net over F₄₉ — Constructive and digital

Digital (12, 39, 62)-net over F₄₉, using

net from sequence [i] based on digital (12, 61)-sequence over F₄₉, using
- Niederreiter sequence [i]

(12, 12+27, 92)-Net over F₄₉ — Digital

Digital (12, 39, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 39, 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]

(12, 12+27, 10291)-Net in Base 49 — Upper bound on s

There is no (12, 39, 10292)-net in base 49, because

1 times m-reduction [i] would yield (12, 38, 10292)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 16896 288915 029586 715434 001601 812095 098074 702553 240084 735875 103425 > 49³⁸ [i]