MinT - Best Known (179−75, 179, s)-Nets in Base 2

Best Known (179−75, 179, s)-Nets in Base 2

(179−75, 179, 60)-Net over F₂ — Constructive and digital

Digital (104, 179, 60)-net over F₂, using

3 times m-reduction [i] based on digital (104, 182, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 91, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(179−75, 179, 76)-Net over F₂ — Digital

Digital (104, 179, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−75, 179, 359)-Net in Base 2 — Upper bound on s

There is no (104, 179, 360)-net in base 2, because

1 times m-reduction [i] would yield (104, 178, 360)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 404944 552818 026750 305302 453909 388596 033412 310315 359053 > 2¹⁷⁸ [i]