MinT - Best Known (29, 29+25, s)-Nets in Base 2

Best Known (29, 29+25, s)-Nets in Base 2

(29, 29+25, 24)-Net over F₂ — Constructive and digital

Digital (29, 54, 24)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 20, 13)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (9, 34, 12)-net over F₂, using
  - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]

(29, 29+25, 25)-Net over F₂ — Digital

Digital (29, 54, 25)-net over F₂, using

t-expansion [i] based on digital (28, 54, 25)-net over F₂, using
- net from sequence [i] based on digital (28, 24)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 28 and N(F) ≥ 25, using
    - a curve from the manYPoints database [i]

(29, 29+25, 95)-Net in Base 2 — Upper bound on s

There is no (29, 54, 96)-net in base 2, because

1 times m-reduction [i] would yield (29, 53, 96)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2⁵³, 96, S₂, 24), but
  - the linear programming bound shows that MÂ â‰¥ 429 789847 275667 421186 486526 017536 / 46352 741187 624885 > 2⁵³ [i]