MinT - Best Known (246−46, 246, s)-Nets in Base 2

Best Known (246−46, 246, s)-Nets in Base 2

(246−46, 246, 320)-Net over F₂ — Constructive and digital

Digital (200, 246, 320)-net over F₂, using

2¹ times duplication [i] based on 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]

(246−46, 246, 763)-Net over F₂ — Digital

Digital (200, 246, 763)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−46, 246, 15603)-Net in Base 2 — Upper bound on s

There is no (200, 246, 15604)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113 149290 413820 157825 860026 892431 942277 462859 537764 743392 830058 100955 594568 > 2²⁴⁶ [i]