MinT - Best Known (13, 13+41, s)-Nets in Base 49

Best Known (13, 13+41, s)-Nets in Base 49

(13, 13+41, 63)-Net over F₄₉ — Constructive and digital

Digital (13, 54, 63)-net over F₄₉, using

net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
- Niederreiter sequence [i]

(13, 13+41, 92)-Net over F₄₉ — Digital

Digital (13, 54, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 54, 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]

(13, 13+41, 5203)-Net in Base 49 — Upper bound on s

There is no (13, 54, 5204)-net in base 49, because

1 times m-reduction [i] would yield (13, 53, 5204)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 381922 497421 836124 060980 524746 340468 872056 931900 921398 376493 498720 408042 293634 358128 981761 > 49⁵³ [i]