MinT - Best Known (29−27, 29, s)-Nets in Base 49

Best Known (29−27, 29, s)-Nets in Base 49

(29−27, 29, 52)-Net over F₄₉ — Constructive and digital

Digital (2, 29, 52)-net over F₄₉, using

net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
- Niederreiter sequence [i]

(29−27, 29, 78)-Net over F₄₉ — Digital

Digital (2, 29, 78)-net over F₄₉, using

net from sequence [i] based on digital (2, 77)-sequence over F₄₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 2 and N(F) ≥ 78, using
  - sharp bound on the number of rational points on curves with genus 2 [i]

(29−27, 29, 488)-Net in Base 49 — Upper bound on s

There is no (2, 29, 489)-net in base 49, because

7 times m-reduction [i] would yield (2, 22, 489)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 15 390880 362184 448267 702889 490736 305633 > 49²² [i]