MinT - Best Known (253−58, 253, s)-Nets in Base 2

Best Known (253−58, 253, s)-Nets in Base 2

(253−58, 253, 206)-Net over F₂ — Constructive and digital

Digital (195, 253, 206)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 37, 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 (158, 216, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 72, 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]

(253−58, 253, 430)-Net over F₂ — Digital

Digital (195, 253, 430)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−58, 253, 4892)-Net in Base 2 — Upper bound on s

There is no (195, 253, 4893)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14484 548860 437154 426333 681822 608830 950157 455101 191909 463435 455698 257392 999418 > 2²⁵³ [i]