MinT - Best Known (139−41, 139, s)-Nets in Base 2

Best Known (139−41, 139, s)-Nets in Base 2

(139−41, 139, 84)-Net over F₂ — Constructive and digital

Digital (98, 139, 84)-net over F₂, using

2¹ times duplication [i] based on digital (97, 138, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 46, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(139−41, 139, 138)-Net over F₂ — Digital

Digital (98, 139, 138)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−41, 139, 962)-Net in Base 2 — Upper bound on s

There is no (98, 139, 963)-net in base 2, because

1 times m-reduction [i] would yield (98, 138, 963)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 350788 573786 393537 956758 800488 909264 073424 > 2¹³⁸ [i]