MinT - Best Known (257−78, 257, s)-Nets in Base 2

Best Known (257−78, 257, s)-Nets in Base 2

(257−78, 257, 132)-Net over F₂ — Constructive and digital

Digital (179, 257, 132)-net over F₂, using

3 times m-reduction [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]

(257−78, 257, 215)-Net over F₂ — Digital

Digital (179, 257, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−78, 257, 1425)-Net in Base 2 — Upper bound on s

There is no (179, 257, 1426)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231586 625936 929672 013384 500655 387363 836424 291286 930810 727996 636305 002263 115616 > 2²⁵⁷ [i]