Best Known (155−28, 155, s)-Nets in Base 8
(155−28, 155, 18727)-Net over F8 — Constructive and digital
Digital (127, 155, 18727)-net over F8, using
- 83 times duplication [i] based on digital (124, 152, 18727)-net over F8, using
- net defined by OOA [i] based on linear OOA(8152, 18727, F8, 28, 28) (dual of [(18727, 28), 524204, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8152, 262178, F8, 28) (dual of [262178, 262026, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 262181, F8, 28) (dual of [262181, 262029, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8152, 262178, F8, 28) (dual of [262178, 262026, 29]-code), using
- net defined by OOA [i] based on linear OOA(8152, 18727, F8, 28, 28) (dual of [(18727, 28), 524204, 29]-NRT-code), using
(155−28, 155, 262190)-Net over F8 — Digital
Digital (127, 155, 262190)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8155, 262190, F8, 28) (dual of [262190, 262035, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(810, 46, F8, 6) (dual of [46, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
(155−28, 155, large)-Net in Base 8 — Upper bound on s
There is no (127, 155, large)-net in base 8, because
- 26 times m-reduction [i] would yield (127, 129, large)-net in base 8, but