MinT - Best Known (112, 196, s)-Nets in Base 2

Best Known (112, 196, s)-Nets in Base 2

(112, 196, 60)-Net over F₂ — Constructive and digital

Digital (112, 196, 60)-net over F₂, using

2 times m-reduction [i] based on digital (112, 198, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 99, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(112, 196, 78)-Net over F₂ — Digital

Digital (112, 196, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 196, 298)-Net in Base 2 — Upper bound on s

There is no (112, 196, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2¹⁹⁶, 299, S₂, 84), but
- adding a parity check bit [i] would yield OA(2¹⁹⁷, 300, S₂, 85), but
  - the linear programming bound shows that MÂ â‰¥ 333445 596634 842101 957662 761369 966680 970228 955880 375209 681209 067512 159971 176505 925710 036206 046927 475988 200870 117376 / 1 055603 696799 631985 996897 950925 994087 362055 971326 408581 > 2¹⁹⁷ [i]