MinT - Best Known (115, 198, s)-Nets in Base 2

Best Known (115, 198, s)-Nets in Base 2

(115, 198, 66)-Net over F₂ — Constructive and digital

Digital (115, 198, 66)-net over F₂, using

2 times m-reduction [i] based on digital (115, 200, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 100, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(115, 198, 82)-Net over F₂ — Digital

Digital (115, 198, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 198, 393)-Net in Base 2 — Upper bound on s

There is no (115, 198, 394)-net in base 2, because

1 times m-reduction [i] would yield (115, 197, 394)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 207063 470936 832369 243912 276564 841852 567768 950019 637025 188460 > 2¹⁹⁷ [i]