MinT - Best Known (178−114, 178, s)-Nets in Base 2

Best Known (178−114, 178, s)-Nets in Base 2

(178−114, 178, 43)-Net over F₂ — Constructive and digital

Digital (64, 178, 43)-net over F₂, using

t-expansion [i] based on digital (59, 178, 43)-net over F₂, using
- net from sequence [i] based on digital (59, 42)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(178−114, 178, 44)-Net over F₂ — Digital

Digital (64, 178, 44)-net over F₂, using

t-expansion [i] based on digital (62, 178, 44)-net over F₂, using
- net from sequence [i] based on digital (62, 43)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 62 and N(F) ≥ 44, using
    - a function field from a table by Niederreiter and Xing [i]

(178−114, 178, 121)-Net in Base 2 — Upper bound on s

There is no (64, 178, 122)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 476821 207888 097716 025737 566871 130674 956426 822268 495833 > 2¹⁷⁸ [i]