MinT - Best Known (259−166, 259, s)-Nets in Base 2

Best Known (259−166, 259, s)-Nets in Base 2

(259−166, 259, 53)-Net over F₂ — Constructive and digital

Digital (93, 259, 53)-net over F₂, using

t-expansion [i] based on digital (90, 259, 53)-net over F₂, using
- net from sequence [i] based on digital (90, 52)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(259−166, 259, 60)-Net over F₂ — Digital

Digital (93, 259, 60)-net over F₂, using

t-expansion [i] based on digital (92, 259, 60)-net over F₂, using
- net from sequence [i] based on digital (92, 59)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 92 and N(F) ≥ 60, using
    - Drinfeld modules of rank 1 [i]

(259−166, 259, 172)-Net in Base 2 — Upper bound on s

There is no (93, 259, 173)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 112543 338283 083734 980598 013129 521977 025373 472275 336334 775944 645526 954657 382400 > 2²⁵⁹ [i]