MinT - Best Known (149−31, 149, s)-Nets in Base 2

Best Known (149−31, 149, s)-Nets in Base 2

(149−31, 149, 260)-Net over F₂ — Constructive and digital

Digital (118, 149, 260)-net over F₂, using

2¹ times duplication [i] based on digital (117, 148, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 37, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(149−31, 149, 366)-Net over F₂ — Digital

Digital (118, 149, 366)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−31, 149, 5974)-Net in Base 2 — Upper bound on s

There is no (118, 149, 5975)-net in base 2, because

1 times m-reduction [i] would yield (118, 148, 5975)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 356 838309 985760 580120 849243 089052 234215 200556 > 2¹⁴⁸ [i]