MinT - Best Known (179, 179+77, s)-Nets in Base 2

Best Known (179, 179+77, s)-Nets in Base 2

(179, 179+77, 132)-Net over F₂ — Constructive and digital

Digital (179, 256, 132)-net over F₂, using

4 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]

(179, 179+77, 219)-Net over F₂ — Digital

Digital (179, 256, 219)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(179, 179+77, 1517)-Net in Base 2 — Upper bound on s

There is no (179, 256, 1518)-net in base 2, because

1 times m-reduction [i] would yield (179, 255, 1518)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 57988 115060 198432 975327 734522 360936 838850 907720 528947 306572 352151 196139 623684 > 2²⁵⁵ [i]