MinT - Best Known (245−46, 245, s)-Nets in Base 2

Best Known (245−46, 245, s)-Nets in Base 2

(245−46, 245, 320)-Net over F₂ — Constructive and digital

Digital (199, 245, 320)-net over F₂, using

trace code for nets [i] based on digital (3, 49, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(245−46, 245, 750)-Net over F₂ — Digital

Digital (199, 245, 750)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−46, 245, 15139)-Net in Base 2 — Upper bound on s

There is no (199, 245, 15140)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56 595842 549789 378475 572245 228896 452954 265857 543955 014925 671040 403804 185544 > 2²⁴⁵ [i]