MinT - Best Known (38, 38+179, s)-Nets in Base 2

Best Known (38, 38+179, s)-Nets in Base 2

(38, 38+179, 24)-Net over F₂ — Constructive and digital

Digital (38, 217, 24)-net over F₂, using

t-expansion [i] based on digital (33, 217, 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]

(38, 38+179, 30)-Net over F₂ — Digital

Digital (38, 217, 30)-net over F₂, using

t-expansion [i] based on digital (36, 217, 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]

(38, 38+179, 48)-Net in Base 2 — Upper bound on s

There is no (38, 217, 49)-net in base 2, because

30 times m-reduction [i] would yield (38, 187, 49)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁸⁷, 49, S₂, 4, 149), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 17262 029772 313372 100548 420913 821082 644281 477472 276094 910464 / 75 > 2¹⁸⁷ [i]