MinT - Best Known (100−85, 100, s)-Nets in Base 2

Best Known (100−85, 100, s)-Nets in Base 2

(100−85, 100, 17)-Net over F₂ — Constructive and digital

Digital (15, 100, 17)-net over F₂, using

net from sequence [i] based on digital (15, 16)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]

(100−85, 100, 22)-Net in Base 2 — Upper bound on s

There is no (15, 100, 23)-net in base 2, because

15 times m-reduction [i] would yield (15, 85, 23)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁸⁵, 23, S₂, 4, 70), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2785 365088 392105 618523 029504 / 71 > 2⁸⁵ [i]