Best Known (120, 142, s)-Nets in Base 8
(120, 142, 190654)-Net over F8 — Constructive and digital
Digital (120, 142, 190654)-net over F8, using
- 81 times duplication [i] based on digital (119, 141, 190654)-net over F8, using
- net defined by OOA [i] based on linear OOA(8141, 190654, F8, 22, 22) (dual of [(190654, 22), 4194247, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8141, 2097194, F8, 22) (dual of [2097194, 2097053, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8140, 2097193, F8, 22) (dual of [2097193, 2097053, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(86, 41, F8, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8140, 2097193, F8, 22) (dual of [2097193, 2097053, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8141, 2097194, F8, 22) (dual of [2097194, 2097053, 23]-code), using
- net defined by OOA [i] based on linear OOA(8141, 190654, F8, 22, 22) (dual of [(190654, 22), 4194247, 23]-NRT-code), using
(120, 142, 2097197)-Net over F8 — Digital
Digital (120, 142, 2097197)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8142, 2097197, F8, 22) (dual of [2097197, 2097055, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8140, 2097193, F8, 22) (dual of [2097193, 2097053, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(86, 41, F8, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(8140, 2097195, F8, 21) (dual of [2097195, 2097055, 22]-code), using Gilbert–Varšamov bound and bm = 8140 > Vbs−1(k−1) = 88832 024506 203105 857369 116146 823581 505821 654825 571638 806212 246469 194127 419857 438710 013356 319289 097625 025719 396236 275056 743812 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 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
- linear OA(8140, 2097193, F8, 22) (dual of [2097193, 2097053, 23]-code), using
- construction X with Varšamov bound [i] based on
(120, 142, large)-Net in Base 8 — Upper bound on s
There is no (120, 142, large)-net in base 8, because
- 20 times m-reduction [i] would yield (120, 122, large)-net in base 8, but