MinT - Best Known (141, 216, s)-Nets in Base 2

Best Known (141, 216, s)-Nets in Base 2

(141, 216, 112)-Net over F₂ — Constructive and digital

Digital (141, 216, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 108, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(141, 216, 136)-Net over F₂ — Digital

Digital (141, 216, 136)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 216, 769)-Net in Base 2 — Upper bound on s

There is no (141, 216, 770)-net in base 2, because

1 times m-reduction [i] would yield (141, 215, 770)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 54755 199352 156108 486888 082356 251705 814895 090276 921885 651229 223488 > 2²¹⁵ [i]