MinT - Best Known (243−49, 243, s)-Nets in Base 2

Best Known (243−49, 243, s)-Nets in Base 2

(243−49, 243, 260)-Net over F₂ — Constructive and digital

Digital (194, 243, 260)-net over F₂, using

t-expansion [i] based on digital (192, 243, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (192, 248, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 62, 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]

(243−49, 243, 595)-Net over F₂ — Digital

Digital (194, 243, 595)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−49, 243, 10599)-Net in Base 2 — Upper bound on s

There is no (194, 243, 10600)-net in base 2, because

1 times m-reduction [i] would yield (194, 242, 10600)-net in base 2, but
- 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]