MinT - Best Known (259−48, 259, s)-Nets in Base 2

Best Known (259−48, 259, s)-Nets in Base 2

(259−48, 259, 320)-Net over F₂ — Constructive and digital

Digital (211, 259, 320)-net over F₂, using

1 times m-reduction [i] based on digital (211, 260, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 52, 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]

(259−48, 259, 820)-Net over F₂ — Digital

Digital (211, 259, 820)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−48, 259, 17341)-Net in Base 2 — Upper bound on s

There is no (211, 259, 17342)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 926764 962555 184635 898963 472035 995498 470230 294168 319811 800656 218634 056226 303081 > 2²⁵⁹ [i]