MinT - Best Known (128, 139, s)-Nets in Base 2

Best Known (128, 139, s)-Nets in Base 2

(128, 139, 2796200)-Net over F₂ — Constructive and digital

Digital (128, 139, 2796200)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹³⁹, 2796200, F₂, 14, 11) (dual of [(2796200, 14), 39146661, 12]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2¹³⁹, 8388601, F₂, 2, 11) (dual of [(8388601, 2), 16777063, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹³⁹, large, F₂, 2, 11), using
    - OOAs constructed from BCH codes [i]

(128, 139, 4194301)-Net over F₂ — Digital

Digital (128, 139, 4194301)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹³⁹, 4194301, F₂, 4, 11) (dual of [(4194301, 4), 16777065, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹³⁹, 8388602, F₂, 2, 11) (dual of [(8388602, 2), 16777065, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹³⁹, large, F₂, 2, 11), using
    - OOAs constructed from BCH codes [i]

(128, 139, large)-Net in Base 2 — Upper bound on s

There is no (128, 139, large)-net in base 2, because

9 times m-reduction [i] would yield (128, 130, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]