Best Known (40, 76, s)-Nets in Base 128
(40, 76, 911)-Net over F128 — Constructive and digital
Digital (40, 76, 911)-net over F128, using
- 1281 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(12875, 911, F128, 36, 36) (dual of [(911, 36), 32721, 37]-NRT-code), using
(40, 76, 5490)-Net over F128 — Digital
Digital (40, 76, 5490)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12876, 5490, F128, 2, 36) (dual of [(5490, 2), 10904, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12876, 8200, F128, 2, 36) (dual of [(8200, 2), 16324, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12876, 16400, F128, 36) (dual of [16400, 16324, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(12876, 16401, F128, 36) (dual of [16401, 16325, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [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(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(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(12876, 16401, F128, 36) (dual of [16401, 16325, 37]-code), using
- OOA 2-folding [i] based on linear OA(12876, 16400, F128, 36) (dual of [16400, 16324, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(12876, 8200, F128, 2, 36) (dual of [(8200, 2), 16324, 37]-NRT-code), using
(40, 76, large)-Net in Base 128 — Upper bound on s
There is no (40, 76, large)-net in base 128, because
- 34 times m-reduction [i] would yield (40, 42, large)-net in base 128, but