MinT - Best Known (241−51, 241, s)-Nets in Base 2

Best Known (241−51, 241, s)-Nets in Base 2

(241−51, 241, 260)-Net over F₂ — Constructive and digital

Digital (190, 241, 260)-net over F₂, using

t-expansion [i] based on digital (189, 241, 260)-net over F₂, using
- 3 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 61, 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]

(241−51, 241, 513)-Net over F₂ — Digital

Digital (190, 241, 513)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−51, 241, 7861)-Net in Base 2 — Upper bound on s

There is no (190, 241, 7862)-net in base 2, because

1 times m-reduction [i] would yield (190, 240, 7862)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 772346 108583 451293 780875 627220 467189 306318 677261 607108 159985 591988 061516 > 2²⁴⁰ [i]