Best Known (141−28, 141, s)-Nets in Base 8
(141−28, 141, 2369)-Net over F8 — Constructive and digital
Digital (113, 141, 2369)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (94, 122, 2341)-net over F8, using
- net defined by OOA [i] based on linear OOA(8122, 2341, F8, 28, 28) (dual of [(2341, 28), 65426, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8122, 32774, F8, 28) (dual of [32774, 32652, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8122, 32779, F8, 28) (dual of [32779, 32657, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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(8122, 32779, F8, 28) (dual of [32779, 32657, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8122, 32774, F8, 28) (dual of [32774, 32652, 29]-code), using
- net defined by OOA [i] based on linear OOA(8122, 2341, F8, 28, 28) (dual of [(2341, 28), 65426, 29]-NRT-code), using
- digital (5, 19, 28)-net over F8, using
(141−28, 141, 4681)-Net in Base 8 — Constructive
(113, 141, 4681)-net in base 8, using
- 81 times duplication [i] based on (112, 140, 4681)-net in base 8, using
- base change [i] based on digital (77, 105, 4681)-net over F16, using
- net defined by OOA [i] based on linear OOA(16105, 4681, F16, 28, 28) (dual of [(4681, 28), 130963, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16105, 65534, F16, 28) (dual of [65534, 65429, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16105, 65534, F16, 28) (dual of [65534, 65429, 29]-code), using
- net defined by OOA [i] based on linear OOA(16105, 4681, F16, 28, 28) (dual of [(4681, 28), 130963, 29]-NRT-code), using
- base change [i] based on digital (77, 105, 4681)-net over F16, using
(141−28, 141, 81193)-Net over F8 — Digital
Digital (113, 141, 81193)-net over F8, using
(141−28, 141, large)-Net in Base 8 — Upper bound on s
There is no (113, 141, large)-net in base 8, because
- 26 times m-reduction [i] would yield (113, 115, large)-net in base 8, but