Best Known (118, 118+28, s)-Nets in Base 8
(118, 118+28, 18725)-Net over F8 — Constructive and digital
Digital (118, 146, 18725)-net over F8, using
- 81 times duplication [i] based on digital (117, 145, 18725)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [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(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
(118, 118+28, 163914)-Net over F8 — Digital
Digital (118, 146, 163914)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8146, 163914, F8, 28) (dual of [163914, 163768, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 262157, F8, 28) (dual of [262157, 262011, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8146, 262157, F8, 28) (dual of [262157, 262011, 29]-code), using
(118, 118+28, large)-Net in Base 8 — Upper bound on s
There is no (118, 146, large)-net in base 8, because
- 26 times m-reduction [i] would yield (118, 120, large)-net in base 8, but