MinT - Best Known (121, 121+9, s)-Nets in Base 2

Best Known (121, 121+9, s)-Nets in Base 2

(121, 121+9, 4194429)-Net over F₂ — Constructive and digital

Digital (121, 130, 4194429)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹³⁰, 4194429, F₂, 9, 9) (dual of [(4194429, 9), 37749731, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2¹³⁰, 4194429, F₂, 8, 9) (dual of [(4194429, 8), 33555302, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁴, 128, F₂, 8, 4) (dual of [(128, 8), 1010, 5]-NRT-code), using
      - appending 4 arbitrary columns [i] based on linear OOA(2¹⁴, 128, F₂, 4, 4) (dual of [(128, 4), 498, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2¹⁴, 128, F₂, 3, 4) (dual of [(128, 3), 370, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (10, 14, 128)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹¹⁶, 4194301, F₂, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁶, large, F₂, 2, 9), using
        OOAs constructed from BCH codes [i]

(121, 121+9, large)-Net over F₂ — Digital

Digital (121, 130, large)-net over F₂, using

2¹³ times duplication [i] based on digital (108, 117, large)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2¹¹⁷, large, F₂, 9, 9), using
  - appending kth column [i] based on linear OOA(2¹¹⁷, large, F₂, 8, 9), using
    - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹¹⁷, large, F₂, 3, 9), using
      - OOAs constructed from BCH codes [i]

(121, 121+9, large)-Net in Base 2 — Upper bound on s

There is no (121, 130, large)-net in base 2, because

7 times m-reduction [i] would yield (121, 123, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]