MinT - Best Known (243−71, 243, s)-Nets in Base 2

Best Known (243−71, 243, s)-Nets in Base 2

(243−71, 243, 138)-Net over F₂ — Constructive and digital

Digital (172, 243, 138)-net over F₂, using

trace code for nets [i] based on digital (10, 81, 46)-net over F₈, using
- net from sequence [i] based on digital (10, 45)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]

(243−71, 243, 224)-Net over F₂ — Digital

Digital (172, 243, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−71, 243, 1626)-Net in Base 2 — Upper bound on s

There is no (172, 243, 1627)-net in base 2, because

1 times m-reduction [i] would yield (172, 242, 1627)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 177418 846187 039965 453079 677101 992297 025345 095875 118599 814530 000138 667068 > 2²⁴² [i]