MinT - Best Known (144−61, 144, s)-Nets in Base 2

Best Known (144−61, 144, s)-Nets in Base 2

(144−61, 144, 54)-Net over F₂ — Constructive and digital

Digital (83, 144, 54)-net over F₂, using

2 times m-reduction [i] based on digital (83, 146, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 73, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(144−61, 144, 62)-Net over F₂ — Digital

Digital (83, 144, 62)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−61, 144, 285)-Net in Base 2 — Upper bound on s

There is no (83, 144, 286)-net in base 2, because

1 times m-reduction [i] would yield (83, 143, 286)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 217107 197022 023558 448070 148348 659143 150712 > 2¹⁴³ [i]