MinT - Best Known (198−140, 198, s)-Nets in Base 2

Best Known (198−140, 198, s)-Nets in Base 2

(198−140, 198, 42)-Net over F₂ — Constructive and digital

Digital (58, 198, 42)-net over F₂, using

t-expansion [i] based on digital (54, 198, 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]

(198−140, 198, 86)-Net in Base 2 — Upper bound on s

There is no (58, 198, 87)-net in base 2, because

31 times m-reduction [i] would yield (58, 167, 87)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁶⁷, 87, S₂, 2, 109), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2993 155353 253689 176481 146537 402947 624255 349848 014848 / 11 > 2¹⁶⁷ [i]