MinT - Best Known (248−46, 248, s)-Nets in Base 2

Best Known (248−46, 248, s)-Nets in Base 2

(248−46, 248, 320)-Net over F₂ — Constructive and digital

Digital (202, 248, 320)-net over F₂, using

2³ 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]

(248−46, 248, 789)-Net over F₂ — Digital

Digital (202, 248, 789)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−46, 248, 16575)-Net in Base 2 — Upper bound on s

There is no (202, 248, 16576)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 452 885091 665701 166923 120095 804969 718123 740312 912933 335267 576836 366385 996173 > 2²⁴⁸ [i]