Best Known (16, 30, s)-Nets in Base 128
(16, 30, 2342)-Net over F128 — Constructive and digital
Digital (16, 30, 2342)-net over F128, using
- net defined by OOA [i] based on linear OOA(12830, 2342, F128, 14, 14) (dual of [(2342, 14), 32758, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12830, 16394, F128, 14) (dual of [16394, 16364, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12830, 16395, F128, 14) (dual of [16395, 16365, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12830, 16395, F128, 14) (dual of [16395, 16365, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12830, 16394, F128, 14) (dual of [16394, 16364, 15]-code), using
(16, 30, 8197)-Net over F128 — Digital
Digital (16, 30, 8197)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12830, 8197, F128, 2, 14) (dual of [(8197, 2), 16364, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12830, 16394, F128, 14) (dual of [16394, 16364, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12830, 16395, F128, 14) (dual of [16395, 16365, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12830, 16395, F128, 14) (dual of [16395, 16365, 15]-code), using
- OOA 2-folding [i] based on linear OA(12830, 16394, F128, 14) (dual of [16394, 16364, 15]-code), using
(16, 30, large)-Net in Base 128 — Upper bound on s
There is no (16, 30, large)-net in base 128, because
- 12 times m-reduction [i] would yield (16, 18, large)-net in base 128, but