MinT - Best Known (2, 2+12, s)-Nets in Base 49

Best Known (2, 2+12, s)-Nets in Base 49

(2, 2+12, 52)-Net over F₄₉ — Constructive and digital

Digital (2, 14, 52)-net over F₄₉, using

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

(2, 2+12, 78)-Net over F₄₉ — Digital

Digital (2, 14, 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]

(2, 2+12, 545)-Net in Base 49 — Upper bound on s

There is no (2, 14, 546)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 463183 532622 377621 990209 > 49¹⁴ [i]