MinT - Best Known (197−83, 197, s)-Nets in Base 2

Best Known (197−83, 197, s)-Nets in Base 2

(197−83, 197, 66)-Net over F₂ — Constructive and digital

Digital (114, 197, 66)-net over F₂, using

1 times m-reduction [i] based on digital (114, 198, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 99, 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]

(197−83, 197, 81)-Net over F₂ — Digital

Digital (114, 197, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−83, 197, 386)-Net in Base 2 — Upper bound on s

There is no (114, 197, 387)-net in base 2, because

1 times m-reduction [i] would yield (114, 196, 387)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 108591 741984 758264 429503 459593 079965 363313 859209 590562 263488 > 2¹⁹⁶ [i]