Information on Result #3280258
(46, 64, 233018)-net in base 64, using 641 times duplication based on (45, 63, 233018)-net in base 64, using
- base change [i] based on digital (36, 54, 233018)-net over F128, using
- net defined by OOA [i] based on linear OOA(12854, 233018, F128, 18, 18) (dual of [(233018, 18), 4194270, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12854, 2097162, F128, 18) (dual of [2097162, 2097108, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12854, 2097163, F128, 18) (dual of [2097163, 2097109, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(12854, 2097163, F128, 18) (dual of [2097163, 2097109, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(12854, 2097162, F128, 18) (dual of [2097162, 2097108, 19]-code), using
- net defined by OOA [i] based on linear OOA(12854, 233018, F128, 18, 18) (dual of [(233018, 18), 4194270, 19]-NRT-code), using
Mode: Constructive.
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | (78, 96, 233018)-net in base 16 | [i] | Base Change | |