MinT - Best Known (235−53, 235, s)-Nets in Base 2

Best Known (235−53, 235, s)-Nets in Base 2

(235−53, 235, 206)-Net over F₂ — Constructive and digital

Digital (182, 235, 206)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 34, 11)-net over F₂, using
  - net from sequence [i] based on digital (8, 10)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 8 and N(F) ≥ 11, using
      - an explicitly constructive algebraic function field [i]
2. digital (148, 201, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 67, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(235−53, 235, 421)-Net over F₂ — Digital

Digital (182, 235, 421)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−53, 235, 5363)-Net in Base 2 — Upper bound on s

There is no (182, 235, 5364)-net in base 2, because

1 times m-reduction [i] would yield (182, 234, 5364)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27642 918273 420524 635076 941461 685211 517130 195949 426301 315272 103863 052140 > 2²³⁴ [i]