Best Known (30, 30+22, s)-Nets in Base 128
(30, 30+22, 1492)-Net over F128 — Constructive and digital
Digital (30, 52, 1492)-net over F128, using
- net defined by OOA [i] based on linear OOA(12852, 1492, F128, 22, 22) (dual of [(1492, 22), 32772, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12852, 16412, F128, 22) (dual of [16412, 16360, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 16413, F128, 22) (dual of [16413, 16361, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(11) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- construction X applied to Ce(21) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 16413, F128, 22) (dual of [16413, 16361, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12852, 16412, F128, 22) (dual of [16412, 16360, 23]-code), using
(30, 30+22, 5958)-Net in Base 128 — Constructive
(30, 52, 5958)-net in base 128, using
- 1 times m-reduction [i] based on (30, 53, 5958)-net in base 128, using
- net defined by OOA [i] based on OOA(12853, 5958, S128, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(12853, 65539, S128, 23), using
- discarding factors based on OA(12853, 65542, S128, 23), using
- discarding parts of the base [i] based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- discarding parts of the base [i] based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- discarding factors based on OA(12853, 65542, S128, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(12853, 65539, S128, 23), using
- net defined by OOA [i] based on OOA(12853, 5958, S128, 23, 23), using
(30, 30+22, 15439)-Net over F128 — Digital
Digital (30, 52, 15439)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12852, 15439, F128, 22) (dual of [15439, 15387, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 16413, F128, 22) (dual of [16413, 16361, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(11) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- construction X applied to Ce(21) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 16413, F128, 22) (dual of [16413, 16361, 23]-code), using
(30, 30+22, large)-Net in Base 128 — Upper bound on s
There is no (30, 52, large)-net in base 128, because
- 20 times m-reduction [i] would yield (30, 32, large)-net in base 128, but