MinT - Best Known (141−30, 141, s)-Nets in Base 2

Best Known (141−30, 141, s)-Nets in Base 2

(141−30, 141, 196)-Net over F₂ — Constructive and digital

Digital (111, 141, 196)-net over F₂, using

2¹ times duplication [i] based on digital (110, 140, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 35, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(141−30, 141, 328)-Net over F₂ — Digital

Digital (111, 141, 328)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−30, 141, 4317)-Net in Base 2 — Upper bound on s

There is no (111, 141, 4318)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 791069 744001 499270 841142 670272 250097 271308 > 2¹⁴¹ [i]