MinT - Best Known (194, 194+48, s)-Nets in Base 2

Best Known (194, 194+48, s)-Nets in Base 2

(194, 194+48, 266)-Net over F₂ — Constructive and digital

Digital (194, 242, 266)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (2, 26, 6)-net over F₂, using
  - net from sequence [i] based on digital (2, 5)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (168, 216, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 54, 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]

(194, 194+48, 624)-Net over F₂ — Digital

Digital (194, 242, 624)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194, 194+48, 10599)-Net in Base 2 — Upper bound on s

There is no (194, 242, 10600)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 070192 654046 566415 727496 212665 487656 359730 884503 840481 022170 820397 130156 > 2²⁴² [i]