MinT - Best Known (12, 12+40, s)-Nets in Base 49

Best Known (12, 12+40, s)-Nets in Base 49

(12, 12+40, 62)-Net over F₄₉ — Constructive and digital

Digital (12, 52, 62)-net over F₄₉, using

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

(12, 12+40, 92)-Net over F₄₉ — Digital

Digital (12, 52, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 52, 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+40, 4281)-Net in Base 49 — Upper bound on s

There is no (12, 52, 4282)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 7793 203341 645190 271560 230023 569178 220777 447658 130894 241317 635729 671066 712713 944314 489729 > 49⁵² [i]