Best Known (120−24, 120, s)-Nets in Base 8
(120−24, 120, 2754)-Net over F8 — Constructive and digital
Digital (96, 120, 2754)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (81, 105, 2730)-net over F8, using
- net defined by OOA [i] based on linear OOA(8105, 2730, F8, 24, 24) (dual of [(2730, 24), 65415, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8105, 32760, F8, 24) (dual of [32760, 32655, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 32767, F8, 24) (dual of [32767, 32662, 25]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 32767, F8, 24) (dual of [32767, 32662, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8105, 32760, F8, 24) (dual of [32760, 32655, 25]-code), using
- net defined by OOA [i] based on linear OOA(8105, 2730, F8, 24, 24) (dual of [(2730, 24), 65415, 25]-NRT-code), using
- digital (3, 15, 24)-net over F8, using
(120−24, 120, 5462)-Net in Base 8 — Constructive
(96, 120, 5462)-net in base 8, using
- base change [i] based on digital (66, 90, 5462)-net over F16, using
- net defined by OOA [i] based on linear OOA(1690, 5462, F16, 24, 24) (dual of [(5462, 24), 130998, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(1690, 65544, F16, 24) (dual of [65544, 65454, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, 65545, F16, 24) (dual of [65545, 65455, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(1689, 65536, F16, 24) (dual of [65536, 65447, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(1690, 65545, F16, 24) (dual of [65545, 65455, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(1690, 65544, F16, 24) (dual of [65544, 65454, 25]-code), using
- net defined by OOA [i] based on linear OOA(1690, 5462, F16, 24, 24) (dual of [(5462, 24), 130998, 25]-NRT-code), using
(120−24, 120, 69375)-Net over F8 — Digital
Digital (96, 120, 69375)-net over F8, using
(120−24, 120, large)-Net in Base 8 — Upper bound on s
There is no (96, 120, large)-net in base 8, because
- 22 times m-reduction [i] would yield (96, 98, large)-net in base 8, but