MinT - Best Known (142−38, 142, s)-Nets in Base 2

Best Known (142−38, 142, s)-Nets in Base 2

(142−38, 142, 135)-Net over F₂ — Constructive and digital

Digital (104, 142, 135)-net over F₂, using

2¹ times duplication [i] based on digital (103, 141, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 47, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(142−38, 142, 179)-Net over F₂ — Digital

Digital (104, 142, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−38, 142, 1381)-Net in Base 2 — Upper bound on s

There is no (104, 142, 1382)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 605355 985135 026663 116093 856137 436142 145140 > 2¹⁴² [i]