Best Known (38, 38+36, s)-Nets in Base 128
(38, 38+36, 910)-Net over F128 — Constructive and digital
Digital (38, 74, 910)-net over F128, using
- 1281 times duplication [i] based on digital (37, 73, 910)-net over F128, using
- t-expansion [i] based on digital (36, 73, 910)-net over F128, using
- net defined by OOA [i] based on linear OOA(12873, 910, F128, 37, 37) (dual of [(910, 37), 33597, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(12873, 16384, F128, 37) (dual of [16384, 16311, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12873, 16381, F128, 37) (dual of [16381, 16308, 38]-code), using
- net defined by OOA [i] based on linear OOA(12873, 910, F128, 37, 37) (dual of [(910, 37), 33597, 38]-NRT-code), using
- t-expansion [i] based on digital (36, 73, 910)-net over F128, using
(38, 38+36, 4754)-Net over F128 — Digital
Digital (38, 74, 4754)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12874, 4754, F128, 3, 36) (dual of [(4754, 3), 14188, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12874, 5465, F128, 3, 36) (dual of [(5465, 3), 16321, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12874, 16395, F128, 36) (dual of [16395, 16321, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(31) [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(12863, 16384, F128, 32) (dual of [16384, 16321, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(35) ⊂ Ce(31) [i] based on
- OOA 3-folding [i] based on linear OA(12874, 16395, F128, 36) (dual of [16395, 16321, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(12874, 5465, F128, 3, 36) (dual of [(5465, 3), 16321, 37]-NRT-code), using
(38, 38+36, large)-Net in Base 128 — Upper bound on s
There is no (38, 74, large)-net in base 128, because
- 34 times m-reduction [i] would yield (38, 40, large)-net in base 128, but