MinT - Best Known (260−57, 260, s)-Nets in Base 2

Best Known (260−57, 260, s)-Nets in Base 2

(260−57, 260, 260)-Net over F₂ — Constructive and digital

Digital (203, 260, 260)-net over F₂, using

t-expansion [i] based on digital (201, 260, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 65, 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]

(260−57, 260, 496)-Net over F₂ — Digital

Digital (203, 260, 496)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−57, 260, 6837)-Net in Base 2 — Upper bound on s

There is no (203, 260, 6838)-net in base 2, because

1 times m-reduction [i] would yield (203, 259, 6838)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 927363 021025 439299 550033 823977 931543 295892 765609 316482 886961 474464 111694 089540 > 2²⁵⁹ [i]