MinT - Best Known (231−138, 231, s)-Nets in Base 2

Best Known (231−138, 231, s)-Nets in Base 2

(231−138, 231, 53)-Net over F₂ — Constructive and digital

Digital (93, 231, 53)-net over F₂, using

t-expansion [i] based on digital (90, 231, 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]

(231−138, 231, 60)-Net over F₂ — Digital

Digital (93, 231, 60)-net over F₂, using

t-expansion [i] based on digital (92, 231, 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]

(231−138, 231, 182)-Net in Base 2 — Upper bound on s

There is no (93, 231, 183)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4470 234097 740054 154376 927432 128922 259432 437922 385546 792639 852020 565240 > 2²³¹ [i]