Best Known (60−30, 60, s)-Nets in Base 128
(60−30, 60, 1092)-Net over F128 — Constructive and digital
Digital (30, 60, 1092)-net over F128, using
- 1 times m-reduction [i] based on digital (30, 61, 1092)-net over F128, using
- net defined by OOA [i] based on linear OOA(12861, 1092, F128, 31, 31) (dual of [(1092, 31), 33791, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
- net defined by OOA [i] based on linear OOA(12861, 1092, F128, 31, 31) (dual of [(1092, 31), 33791, 32]-NRT-code), using
(60−30, 60, 4097)-Net over F128 — Digital
Digital (30, 60, 4097)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12860, 4097, F128, 4, 30) (dual of [(4097, 4), 16328, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12860, 16388, F128, 30) (dual of [16388, 16328, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(12860, 16389, F128, 30) (dual of [16389, 16329, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(12860, 16389, F128, 30) (dual of [16389, 16329, 31]-code), using
- OOA 4-folding [i] based on linear OA(12860, 16388, F128, 30) (dual of [16388, 16328, 31]-code), using
(60−30, 60, large)-Net in Base 128 — Upper bound on s
There is no (30, 60, large)-net in base 128, because
- 28 times m-reduction [i] would yield (30, 32, large)-net in base 128, but