Best Known (141, 141+27, s)-Nets in Base 8
(141, 141+27, 161321)-Net over F8 — Constructive and digital
Digital (141, 168, 161321)-net over F8, using
- 82 times duplication [i] based on digital (139, 166, 161321)-net over F8, using
- net defined by OOA [i] based on linear OOA(8166, 161321, F8, 27, 27) (dual of [(161321, 27), 4355501, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8166, 2097174, F8, 27) (dual of [2097174, 2097008, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 2097177, F8, 27) (dual of [2097177, 2097011, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [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(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8166, 2097177, F8, 27) (dual of [2097177, 2097011, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8166, 2097174, F8, 27) (dual of [2097174, 2097008, 28]-code), using
- net defined by OOA [i] based on linear OOA(8166, 161321, F8, 27, 27) (dual of [(161321, 27), 4355501, 28]-NRT-code), using
(141, 141+27, 1567345)-Net over F8 — Digital
Digital (141, 168, 1567345)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8168, 1567345, F8, 27) (dual of [1567345, 1567177, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8168, 2097186, F8, 27) (dual of [2097186, 2097018, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(21) [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(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(86, 34, F8, 4) (dual of [34, 28, 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(26) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8168, 2097186, F8, 27) (dual of [2097186, 2097018, 28]-code), using
(141, 141+27, large)-Net in Base 8 — Upper bound on s
There is no (141, 168, large)-net in base 8, because
- 25 times m-reduction [i] would yield (141, 143, large)-net in base 8, but