Best Known (125−25, 125, s)-Nets in Base 8
(125−25, 125, 2764)-Net over F8 — Constructive and digital
Digital (100, 125, 2764)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (81, 106, 2730)-net over F8, using
- net defined by OOA [i] based on linear OOA(8106, 2730, F8, 25, 25) (dual of [(2730, 25), 68144, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8106, 32761, F8, 25) (dual of [32761, 32655, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8106, 32761, F8, 25) (dual of [32761, 32655, 26]-code), using
- net defined by OOA [i] based on linear OOA(8106, 2730, F8, 25, 25) (dual of [(2730, 25), 68144, 26]-NRT-code), using
- digital (7, 19, 34)-net over F8, using
(125−25, 125, 5461)-Net in Base 8 — Constructive
(100, 125, 5461)-net in base 8, using
- 81 times duplication [i] based on (99, 124, 5461)-net in base 8, using
- base change [i] based on digital (68, 93, 5461)-net over F16, using
- net defined by OOA [i] based on linear OOA(1693, 5461, F16, 25, 25) (dual of [(5461, 25), 136432, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1693, 65533, F16, 25) (dual of [65533, 65440, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1693, 65533, F16, 25) (dual of [65533, 65440, 26]-code), using
- net defined by OOA [i] based on linear OOA(1693, 5461, F16, 25, 25) (dual of [(5461, 25), 136432, 26]-NRT-code), using
- base change [i] based on digital (68, 93, 5461)-net over F16, using
(125−25, 125, 70783)-Net over F8 — Digital
Digital (100, 125, 70783)-net over F8, using
(125−25, 125, large)-Net in Base 8 — Upper bound on s
There is no (100, 125, large)-net in base 8, because
- 23 times m-reduction [i] would yield (100, 102, large)-net in base 8, but