MinT - Best Known (100−78, 100, s)-Nets in Base 2

Best Known (100−78, 100, s)-Nets in Base 2

(100−78, 100, 21)-Net over F₂ — Constructive and digital

Digital (22, 100, 21)-net over F₂, using

t-expansion [i] based on digital (21, 100, 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]

(100−78, 100, 32)-Net in Base 2 — Upper bound on s

There is no (22, 100, 33)-net in base 2, because

9 times m-reduction [i] would yield (22, 91, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁹¹, 33, S₂, 3, 69), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 316912 650057 057350 374175 801344 / 105 > 2⁹¹ [i]