Best Known (145, 172, s)-Nets in Base 8
(145, 172, 161322)-Net over F8 — Constructive and digital
Digital (145, 172, 161322)-net over F8, using
- 83 times duplication [i] based on digital (142, 169, 161322)-net over F8, using
- net defined by OOA [i] based on linear OOA(8169, 161322, F8, 27, 27) (dual of [(161322, 27), 4355525, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8169, 2097187, F8, 27) (dual of [2097187, 2097018, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, 2097194, F8, 27) (dual of [2097194, 2097025, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 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(26) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8169, 2097194, F8, 27) (dual of [2097194, 2097025, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8169, 2097187, F8, 27) (dual of [2097187, 2097018, 28]-code), using
- net defined by OOA [i] based on linear OOA(8169, 161322, F8, 27, 27) (dual of [(161322, 27), 4355525, 28]-NRT-code), using
(145, 172, 2097204)-Net over F8 — Digital
Digital (145, 172, 2097204)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8172, 2097204, F8, 27) (dual of [2097204, 2097032, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 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(26) ⊂ Ce(19) [i] based on
(145, 172, large)-Net in Base 8 — Upper bound on s
There is no (145, 172, large)-net in base 8, because
- 25 times m-reduction [i] would yield (145, 147, large)-net in base 8, but