MinT - Best Known (238−44, 238, s)-Nets in Base 2

Best Known (238−44, 238, s)-Nets in Base 2

(238−44, 238, 320)-Net over F₂ — Constructive and digital

Digital (194, 238, 320)-net over F₂, using

2³ times duplication [i] based on digital (191, 235, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 47, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(238−44, 238, 772)-Net over F₂ — Digital

Digital (194, 238, 772)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−44, 238, 16314)-Net in Base 2 — Upper bound on s

There is no (194, 238, 16315)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 441718 718325 855662 239802 389405 101764 086040 763952 954526 003925 258962 959994 > 2²³⁸ [i]