MinT - Best Known (91, 91+71, s)-Nets in Base 2

Best Known (91, 91+71, s)-Nets in Base 2

(91, 91+71, 54)-Net over F₂ — Constructive and digital

Digital (91, 162, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 81, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(91, 91+71, 63)-Net over F₂ — Digital

Digital (91, 162, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+71, 288)-Net in Base 2 — Upper bound on s

There is no (91, 162, 289)-net in base 2, because

1 times m-reduction [i] would yield (91, 161, 289)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 026232 290403 531690 817731 275652 462961 036232 662344 > 2¹⁶¹ [i]