MinT - Best Known (244−73, 244, s)-Nets in Base 2

Best Known (244−73, 244, s)-Nets in Base 2

(244−73, 244, 132)-Net over F₂ — Constructive and digital

Digital (171, 244, 132)-net over F₂, using

trace code for nets [i] based on digital (49, 122, 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]

(244−73, 244, 213)-Net over F₂ — Digital

Digital (171, 244, 213)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−73, 244, 1484)-Net in Base 2 — Upper bound on s

There is no (171, 244, 1485)-net in base 2, because

1 times m-reduction [i] would yield (171, 243, 1485)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 337274 715440 210743 218201 273331 535329 841086 022654 146861 352600 763487 905918 > 2²⁴³ [i]