MinT - Best Known (209−172, 209, s)-Nets in Base 2

Best Known (209−172, 209, s)-Nets in Base 2

(209−172, 209, 24)-Net over F₂ — Constructive and digital

Digital (37, 209, 24)-net over F₂, using

t-expansion [i] based on digital (33, 209, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(209−172, 209, 30)-Net over F₂ — Digital

Digital (37, 209, 30)-net over F₂, using

t-expansion [i] based on digital (36, 209, 30)-net over F₂, using
- net from sequence [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

(209−172, 209, 47)-Net in Base 2 — Upper bound on s

There is no (37, 209, 48)-net in base 2, because

26 times m-reduction [i] would yield (37, 183, 48)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁸³, 48, S₂, 4, 146), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 2249 703453 991124 844070 053435 856653 881552 309031 365527 994368 / 147 > 2¹⁸³ [i]