MinT - Best Known (121, 121+91, s)-Nets in Base 2

Best Known (121, 121+91, s)-Nets in Base 2

(121, 121+91, 66)-Net over F₂ — Constructive and digital

Digital (121, 212, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 106, 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]

(121, 121+91, 83)-Net over F₂ — Digital

Digital (121, 212, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+91, 391)-Net in Base 2 — Upper bound on s

There is no (121, 212, 392)-net in base 2, because

1 times m-reduction [i] would yield (121, 211, 392)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3349 359524 189660 435463 704415 383361 402788 992972 675541 963825 378384 > 2²¹¹ [i]