MinT - Best Known (42, 42+156, s)-Nets in Base 2

Best Known (42, 42+156, s)-Nets in Base 2

(42, 42+156, 33)-Net over F₂ — Constructive and digital

Digital (42, 198, 33)-net over F₂, using

t-expansion [i] based on digital (39, 198, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(42, 42+156, 55)-Net in Base 2 — Upper bound on s

There is no (42, 198, 56)-net in base 2, because

37 times m-reduction [i] would yield (42, 161, 56)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁶¹, 56, S₂, 3, 119), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 46 768052 394588 893382 517914 646921 056628 989841 375232 / 15 > 2¹⁶¹ [i]