MinT - Best Known (260−78, 260, s)-Nets in Base 2

Best Known (260−78, 260, s)-Nets in Base 2

(260−78, 260, 132)-Net over F₂ — Constructive and digital

Digital (182, 260, 132)-net over F₂, using

t-expansion [i] based on digital (179, 260, 132)-net over F₂, using
- trace code for nets [i] based on digital (49, 130, 66)-net over F₄, using
  - net from sequence [i] based on digital (49, 65)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
      - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−78, 260, 223)-Net over F₂ — Digital

Digital (182, 260, 223)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−78, 260, 1507)-Net in Base 2 — Upper bound on s

There is no (182, 260, 1508)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 891663 856806 306713 417196 771595 528113 137842 301689 892260 287574 240015 543794 789344 > 2²⁶⁰ [i]