MinT - Best Known (99−70, 99, s)-Nets in Base 2

Best Known (99−70, 99, s)-Nets in Base 2

(99−70, 99, 21)-Net over F₂ — Constructive and digital

Digital (29, 99, 21)-net over F₂, using

t-expansion [i] based on digital (21, 99, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(99−70, 99, 25)-Net over F₂ — Digital

Digital (29, 99, 25)-net over F₂, using

t-expansion [i] based on digital (28, 99, 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]

(99−70, 99, 46)-Net in Base 2 — Upper bound on s

There is no (29, 99, 47)-net in base 2, because

11 times m-reduction [i] would yield (29, 88, 47)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁸⁸, 47, S₂, 2, 59), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1237 940039 285380 274899 124224 / 3 > 2⁸⁸ [i]