Best Known (21, 21+18, s)-Nets in Base 128
(21, 21+18, 1822)-Net over F128 — Constructive and digital
Digital (21, 39, 1822)-net over F128, using
- net defined by OOA [i] based on linear OOA(12839, 1822, F128, 18, 18) (dual of [(1822, 18), 32757, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1284, 14, F128, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- OA 9-folding and stacking [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
(21, 21+18, 7969)-Net over F128 — Digital
Digital (21, 39, 7969)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12839, 7969, F128, 2, 18) (dual of [(7969, 2), 15899, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12839, 8199, F128, 2, 18) (dual of [(8199, 2), 16359, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1284, 14, F128, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- OOA 2-folding [i] based on linear OA(12839, 16398, F128, 18) (dual of [16398, 16359, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(12839, 8199, F128, 2, 18) (dual of [(8199, 2), 16359, 19]-NRT-code), using
(21, 21+18, large)-Net in Base 128 — Upper bound on s
There is no (21, 39, large)-net in base 128, because
- 16 times m-reduction [i] would yield (21, 23, large)-net in base 128, but