MinT - Best Known (258−48, 258, s)-Nets in Base 2

Best Known (258−48, 258, s)-Nets in Base 2

(258−48, 258, 320)-Net over F₂ — Constructive and digital

Digital (210, 258, 320)-net over F₂, using

2³ times duplication [i] based on digital (207, 255, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 51, 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]

(258−48, 258, 807)-Net over F₂ — Digital

Digital (210, 258, 807)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−48, 258, 16846)-Net in Base 2 — Upper bound on s

There is no (210, 258, 16847)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 463186 075303 524840 841621 513700 418781 207159 777516 800282 248489 120011 103406 476548 > 2²⁵⁸ [i]