MinT - Best Known (123, 133, s)-Nets in Base 2

Best Known (123, 133, s)-Nets in Base 2

(123, 133, 2097151)-Net over F₂ — Constructive and digital

Digital (123, 133, 2097151)-net over F₂, using

1 times m-reduction [i] based on digital (123, 134, 2097151)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2¹³⁴, 2097151, F₂, 15, 11) (dual of [(2097151, 15), 31457131, 12]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹³⁴, 4194303, F₂, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(123, 133, 4194302)-Net over F₂ — Digital

Digital (123, 133, 4194302)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹³³, 4194302, F₂, 3, 10) (dual of [(4194302, 3), 12582773, 11]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2¹³⁴, 4194303, F₂, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
  - OOAs constructed from BCH codes [i]

(123, 133, large)-Net in Base 2 — Upper bound on s

There is no (123, 133, large)-net in base 2, because

8 times m-reduction [i] would yield (123, 125, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]