MinT - Best Known (171−46, 171, s)-Nets in Base 2

Best Known (171−46, 171, s)-Nets in Base 2

(171−46, 171, 144)-Net over F₂ — Constructive and digital

Digital (125, 171, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 57, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(171−46, 171, 204)-Net over F₂ — Digital

Digital (125, 171, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−46, 171, 1597)-Net in Base 2 — Upper bound on s

There is no (125, 171, 1598)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3006 853689 931087 106220 851613 067214 558370 741618 830448 > 2¹⁷¹ [i]