Best Known (75−36, 75, s)-Nets in Base 128
(75−36, 75, 911)-Net over F128 — Constructive and digital
Digital (39, 75, 911)-net over F128, using
- net defined by OOA [i] based on linear OOA(12875, 911, F128, 36, 36) (dual of [(911, 36), 32721, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(30) [i] based on
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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]
- 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(35) ⊂ Ce(30) [i] based on
- OA 18-folding and stacking [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
(75−36, 75, 5466)-Net over F128 — Digital
Digital (39, 75, 5466)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12875, 5466, F128, 3, 36) (dual of [(5466, 3), 16323, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(30) [i] based on
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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]
- 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(35) ⊂ Ce(30) [i] based on
- OOA 3-folding [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
(75−36, 75, large)-Net in Base 128 — Upper bound on s
There is no (39, 75, large)-net in base 128, because
- 34 times m-reduction [i] would yield (39, 41, large)-net in base 128, but