MinT - Best Known (244−46, 244, s)-Nets in Base 2

Best Known (244−46, 244, s)-Nets in Base 2

(244−46, 244, 275)-Net over F₂ — Constructive and digital

Digital (198, 244, 275)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (13, 36, 15)-net over F₂, using
  - net from sequence [i] based on digital (13, 14)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 13 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]
2. digital (162, 208, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 52, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(244−46, 244, 738)-Net over F₂ — Digital

Digital (198, 244, 738)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−46, 244, 14688)-Net in Base 2 — Upper bound on s

There is no (198, 244, 14689)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 274598 848724 657289 177026 104750 232460 256386 548070 092270 554638 030379 336192 > 2²⁴⁴ [i]