MinT - Best Known (258−44, 258, s)-Nets in Base 2

Best Known (258−44, 258, s)-Nets in Base 2

(258−44, 258, 490)-Net over F₂ — Constructive and digital

Digital (214, 258, 490)-net over F₂, using

2³ times duplication [i] based on digital (211, 255, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 51, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(258−44, 258, 1092)-Net over F₂ — Digital

Digital (214, 258, 1092)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−44, 258, 30665)-Net in Base 2 — Upper bound on s

There is no (214, 258, 30666)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 463239 880052 785358 897855 192731 197540 017429 848368 745957 487907 493094 888127 372368 > 2²⁵⁸ [i]