MinT - Best Known (35−11, 35, s)-Nets in Base 2

Best Known (35−11, 35, s)-Nets in Base 2

(35−11, 35, 50)-Net over F₂ — Constructive and digital

Digital (24, 35, 50)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 11, 26)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (13, 24, 25)-net over F₂, using
  - 1 times m-reduction [i] based on digital (13, 25, 25)-net over F₂, using
    - a shift-net [i]

(35−11, 35, 51)-Net over F₂ — Digital

Digital (24, 35, 51)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³⁵, 51, F₂, 2, 11) (dual of [(51, 2), 67, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2³⁵, 102, F₂, 11) (dual of [102, 67, 12]-code), using
  - adding a parity check bit [i] based on linear OA(2³⁴, 101, F₂, 10) (dual of [101, 67, 11]-code), using
    - a â€œGraâ€ code from Grasslâ€™s database [i]

(35−11, 35, 283)-Net in Base 2 — Upper bound on s

There is no (24, 35, 284)-net in base 2, because

1 times m-reduction [i] would yield (24, 34, 284)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17368 016238 > 2³⁴ [i]