Best Known (33−16, 33, s)-Nets in Base 128
(33−16, 33, 2049)-Net over F128 — Constructive and digital
Digital (17, 33, 2049)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 2049, F128, 16, 16) (dual of [(2049, 16), 32751, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(12833, 16392, F128, 16) (dual of [16392, 16359, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OA 8-folding and stacking [i] based on linear OA(12833, 16392, F128, 16) (dual of [16392, 16359, 17]-code), using
(33−16, 33, 5464)-Net over F128 — Digital
Digital (17, 33, 5464)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12833, 5464, F128, 3, 16) (dual of [(5464, 3), 16359, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12833, 16392, F128, 16) (dual of [16392, 16359, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OOA 3-folding [i] based on linear OA(12833, 16392, F128, 16) (dual of [16392, 16359, 17]-code), using
(33−16, 33, large)-Net in Base 128 — Upper bound on s
There is no (17, 33, large)-net in base 128, because
- 14 times m-reduction [i] would yield (17, 19, large)-net in base 128, but