MinT - Best Known (48, 54, s)-Nets in Base 2

Best Known (48, 54, s)-Nets in Base 2

(48, 54, 131071)-Net over F₂ — Constructive and digital

Digital (48, 54, 131071)-net over F₂, using

2¹ times duplication [i] based on digital (47, 53, 131071)-net over F₂, using
- t-expansion [i] based on digital (46, 53, 131071)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]

(48, 54, 131072)-Net over F₂ — Digital

Digital (48, 54, 131072)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁵⁴, 131072, F₂, 6, 6) (dual of [(131072, 6), 786378, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁵⁴, 131072, F₂, 5, 6) (dual of [(131072, 5), 655306, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵⁴, 131072, F₂, 2, 6) (dual of [(131072, 2), 262090, 7]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁵², 131071, F₂, 2, 6) (dual of [(131071, 2), 262090, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
        1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]

(48, 54, 476343)-Net in Base 2 — Upper bound on s

There is no (48, 54, 476344)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 18014 482385 600933 > 2⁵⁴ [i]