MinT - Best Known (135, 135+38, s)-Nets in Base 2

Best Known (135, 135+38, s)-Nets in Base 2

(135, 135+38, 196)-Net over F₂ — Constructive and digital

Digital (135, 173, 196)-net over F₂, using

2¹ times duplication [i] based on digital (134, 172, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 43, 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]

(135, 135+38, 350)-Net over F₂ — Digital

Digital (135, 173, 350)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+38, 4338)-Net in Base 2 — Upper bound on s

There is no (135, 173, 4339)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11973 803454 109370 719808 924284 044408 862191 876416 382386 > 2¹⁷³ [i]