MinT - Best Known (220−163, 220, s)-Nets in Base 2

Best Known (220−163, 220, s)-Nets in Base 2

(220−163, 220, 42)-Net over F₂ — Constructive and digital

Digital (57, 220, 42)-net over F₂, using

t-expansion [i] based on digital (54, 220, 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]

(220−163, 220, 73)-Net in Base 2 — Upper bound on s

There is no (57, 220, 74)-net in base 2, because

6 times m-reduction [i] would yield (57, 214, 74)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²¹⁴, 74, S₂, 3, 157), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2 527495 000045 372480 750032 664408 090375 653482 289613 178670 103463 460864 / 79 > 2²¹⁴ [i]