MinT - Best Known (126, 126+37, s)-Nets in Base 2

Best Known (126, 126+37, s)-Nets in Base 2

(126, 126+37, 195)-Net over F₂ — Constructive and digital

Digital (126, 163, 195)-net over F₂, using

5 times m-reduction [i] based on digital (126, 168, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 56, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(126, 126+37, 305)-Net over F₂ — Digital

Digital (126, 163, 305)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+37, 3840)-Net in Base 2 — Upper bound on s

There is no (126, 163, 3841)-net in base 2, because

1 times m-reduction [i] would yield (126, 162, 3841)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 851112 861027 543280 731658 202164 392290 252677 264064 > 2¹⁶² [i]