MinT - Best Known (36−29, 36, s)-Nets in Base 49

Best Known (36−29, 36, s)-Nets in Base 49

(36−29, 36, 57)-Net over F₄₉ — Constructive and digital

Digital (7, 36, 57)-net over F₄₉, using

net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
- Niederreiter sequence [i]

(36−29, 36, 92)-Net over F₄₉ — Digital

Digital (7, 36, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 36, 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]

(36−29, 36, 2110)-Net in Base 49 — Upper bound on s

There is no (7, 36, 2111)-net in base 49, because

1 times m-reduction [i] would yield (7, 35, 2111)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 144318 042279 560875 500781 297611 130749 378767 974372 280745 805153 > 49³⁵ [i]