MinT - Best Known (260−80, 260, s)-Nets in Base 2

Best Known (260−80, 260, s)-Nets in Base 2

(260−80, 260, 132)-Net over F₂ — Constructive and digital

Digital (180, 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]

(260−80, 260, 210)-Net over F₂ — Digital

Digital (180, 260, 210)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−80, 260, 1368)-Net in Base 2 — Upper bound on s

There is no (180, 260, 1369)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 862261 157114 832808 130783 046722 063432 874620 783615 284319 306601 144880 732231 519758 > 2²⁶⁰ [i]