MinT - Best Known (162−106, 162, s)-Nets in Base 2

Best Known (162−106, 162, s)-Nets in Base 2

(162−106, 162, 42)-Net over F₂ — Constructive and digital

Digital (56, 162, 42)-net over F₂, using

t-expansion [i] based on digital (54, 162, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(162−106, 162, 83)-Net in Base 2 — Upper bound on s

There is no (56, 162, 84)-net in base 2, because

1 times m-reduction [i] would yield (56, 161, 84)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁶¹, 84, S₂, 2, 105), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 187 072209 578355 573530 071658 587684 226515 959365 500928 / 53 > 2¹⁶¹ [i]