MinT - Best Known (91, 91+49, s)-Nets in Base 2

Best Known (91, 91+49, s)-Nets in Base 2

(91, 91+49, 68)-Net over F₂ — Constructive and digital

Digital (91, 140, 68)-net over F₂, using

trace code for nets [i] based on digital (21, 70, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(91, 91+49, 93)-Net over F₂ — Digital

Digital (91, 140, 93)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+49, 508)-Net in Base 2 — Upper bound on s

There is no (91, 140, 509)-net in base 2, because

1 times m-reduction [i] would yield (91, 139, 509)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 710687 249381 468030 913470 363121 359485 685741 > 2¹³⁹ [i]