MinT - Best Known (244−89, 244, s)-Nets in Base 2

Best Known (244−89, 244, s)-Nets in Base 2

(244−89, 244, 112)-Net over F₂ — Constructive and digital

Digital (155, 244, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 122, 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]

(244−89, 244, 135)-Net over F₂ — Digital

Digital (155, 244, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−89, 244, 730)-Net in Base 2 — Upper bound on s

There is no (155, 244, 731)-net in base 2, because

1 times m-reduction [i] would yield (155, 243, 731)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 814463 077959 515177 731836 156559 989912 940100 227362 819745 070300 767648 361880 > 2²⁴³ [i]