Best Known (209, 235, s)-Nets in Base 2
(209, 235, 20166)-Net over F2 — Constructive and digital
Digital (209, 235, 20166)-net over F2, using
- net defined by OOA [i] based on linear OOA(2235, 20166, F2, 26, 26) (dual of [(20166, 26), 524081, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2235, 262158, F2, 26) (dual of [262158, 261923, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2235, 262162, F2, 26) (dual of [262162, 261927, 27]-code), using
- 1 times truncation [i] based on linear OA(2236, 262163, F2, 27) (dual of [262163, 261927, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2236, 262163, F2, 27) (dual of [262163, 261927, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2235, 262162, F2, 26) (dual of [262162, 261927, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2235, 262158, F2, 26) (dual of [262158, 261923, 27]-code), using
(209, 235, 37451)-Net over F2 — Digital
Digital (209, 235, 37451)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2235, 37451, F2, 7, 26) (dual of [(37451, 7), 261922, 27]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2235, 262157, F2, 26) (dual of [262157, 261922, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2235, 262162, F2, 26) (dual of [262162, 261927, 27]-code), using
- 1 times truncation [i] based on linear OA(2236, 262163, F2, 27) (dual of [262163, 261927, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2236, 262163, F2, 27) (dual of [262163, 261927, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2235, 262162, F2, 26) (dual of [262162, 261927, 27]-code), using
- OOA 7-folding [i] based on linear OA(2235, 262157, F2, 26) (dual of [262157, 261922, 27]-code), using
(209, 235, 1567101)-Net in Base 2 — Upper bound on s
There is no (209, 235, 1567102)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 55214 428060 564215 513830 491317 716423 708690 959609 352455 902937 423287 381765 > 2235 [i]