Best Known (44−22, 44, s)-Nets in Base 128
(44−22, 44, 1489)-Net over F128 — Constructive and digital
Digital (22, 44, 1489)-net over F128, using
- 1 times m-reduction [i] based on digital (22, 45, 1489)-net over F128, using
- net defined by OOA [i] based on linear OOA(12845, 1489, F128, 23, 23) (dual of [(1489, 23), 34202, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12845, 16380, F128, 23) (dual of [16380, 16335, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12845, 16380, F128, 23) (dual of [16380, 16335, 24]-code), using
- net defined by OOA [i] based on linear OOA(12845, 1489, F128, 23, 23) (dual of [(1489, 23), 34202, 24]-NRT-code), using
(44−22, 44, 4097)-Net over F128 — Digital
Digital (22, 44, 4097)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12844, 4097, F128, 4, 22) (dual of [(4097, 4), 16344, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12844, 16388, F128, 22) (dual of [16388, 16344, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 16389, F128, 22) (dual of [16389, 16345, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [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(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12844, 16389, F128, 22) (dual of [16389, 16345, 23]-code), using
- OOA 4-folding [i] based on linear OA(12844, 16388, F128, 22) (dual of [16388, 16344, 23]-code), using
(44−22, 44, large)-Net in Base 128 — Upper bound on s
There is no (22, 44, large)-net in base 128, because
- 20 times m-reduction [i] would yield (22, 24, large)-net in base 128, but