Best Known (122, 143, s)-Nets in Base 8
(122, 143, 209744)-Net over F8 — Constructive and digital
Digital (122, 143, 209744)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 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 (107, 128, 209716)-net over F8, using
- net defined by OOA [i] based on linear OOA(8128, 209716, F8, 21, 21) (dual of [(209716, 21), 4403908, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8128, 2097161, F8, 21) (dual of [2097161, 2097033, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8128, 2097168, F8, 21) (dual of [2097168, 2097040, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8127, 2097153, F8, 21) (dual of [2097153, 2097026, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8128, 2097168, F8, 21) (dual of [2097168, 2097040, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8128, 2097161, F8, 21) (dual of [2097161, 2097033, 22]-code), using
- net defined by OOA [i] based on linear OOA(8128, 209716, F8, 21, 21) (dual of [(209716, 21), 4403908, 22]-NRT-code), using
- digital (5, 15, 28)-net over F8, using
(122, 143, 209748)-Net in Base 8 — Constructive
(122, 143, 209748)-net in base 8, using
- (u, u+v)-construction [i] based on
- (6, 16, 33)-net in base 8, using
- base change [i] based on digital (2, 12, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- base change [i] based on digital (2, 12, 33)-net over F16, using
- digital (106, 127, 209715)-net over F8, using
- net defined by OOA [i] based on linear OOA(8127, 209715, F8, 21, 21) (dual of [(209715, 21), 4403888, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8127, 2097151, F8, 21) (dual of [2097151, 2097024, 22]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8127, 2097151, F8, 21) (dual of [2097151, 2097024, 22]-code), using
- net defined by OOA [i] based on linear OOA(8127, 209715, F8, 21, 21) (dual of [(209715, 21), 4403888, 22]-NRT-code), using
- (6, 16, 33)-net in base 8, using
(122, 143, 3398622)-Net over F8 — Digital
Digital (122, 143, 3398622)-net over F8, using
(122, 143, large)-Net in Base 8 — Upper bound on s
There is no (122, 143, large)-net in base 8, because
- 19 times m-reduction [i] would yield (122, 124, large)-net in base 8, but