MinT - Best Known (157, 222, s)-Nets in Base 2

Best Known (157, 222, s)-Nets in Base 2

(157, 222, 135)-Net over F₂ — Constructive and digital

Digital (157, 222, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 74, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(157, 222, 207)-Net over F₂ — Digital

Digital (157, 222, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 222, 1487)-Net in Base 2 — Upper bound on s

There is no (157, 222, 1488)-net in base 2, because

1 times m-reduction [i] would yield (157, 221, 1488)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 418464 327937 543902 573603 960837 822153 126701 112897 735402 051896 901282 > 2²²¹ [i]