MinT - Best Known (150−31, 150, s)-Nets in Base 2

Best Known (150−31, 150, s)-Nets in Base 2

(150−31, 150, 260)-Net over F₂ — Constructive and digital

Digital (119, 150, 260)-net over F₂, using

2² 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]

(150−31, 150, 376)-Net over F₂ — Digital

Digital (119, 150, 376)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−31, 150, 6258)-Net in Base 2 — Upper bound on s

There is no (119, 150, 6259)-net in base 2, because

1 times m-reduction [i] would yield (119, 149, 6259)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 714 325482 693003 359921 060576 415893 437384 149080 > 2¹⁴⁹ [i]