MinT - Best Known (8, 8+29, s)-Nets in Base 49

Best Known (8, 8+29, s)-Nets in Base 49

(8, 8+29, 58)-Net over F₄₉ — Constructive and digital

Digital (8, 37, 58)-net over F₄₉, using

net from sequence [i] based on digital (8, 57)-sequence over F₄₉, using
- Niederreiter sequence [i]

(8, 8+29, 92)-Net over F₄₉ — Digital

Digital (8, 37, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 37, 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]

(8, 8+29, 2788)-Net in Base 49 — Upper bound on s

There is no (8, 37, 2789)-net in base 49, because

1 times m-reduction [i] would yield (8, 36, 2789)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 7 047392 058767 493190 628270 081201 450725 751550 523039 014306 563617 > 49³⁶ [i]