Information on Result #1729096
Digital (116, 142, 52436)-net over F8, using net defined by OOA based on linear OOA(8142, 52436, F8, 33, 26) (dual of [(52436, 33), 1730246, 27]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8142, 262181, F8, 3, 26) (dual of [(262181, 3), 786401, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8142, 262184, F8, 3, 26) (dual of [(262184, 3), 786410, 27]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8142, 262184, F8, 26) (dual of [262184, 262042, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8140, 262182, F8, 24) (dual of [262182, 262042, 25]-code), using Gilbert–Varšamov bound and bm = 8140 > Vbs−1(k−1) = 44 892603 789316 089569 088653 481570 084917 649643 136163 701904 756468 834255 430563 880674 177276 023366 324579 938010 837769 807032 269664 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8142, 262184, F8, 26) (dual of [262184, 262042, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(8142, 262184, F8, 3, 26) (dual of [(262184, 3), 786410, 27]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.