Best Known (144−28, 144, s)-Nets in Base 8
(144−28, 144, 2385)-Net over F8 — Constructive and digital
Digital (116, 144, 2385)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (93, 121, 2340)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 2340, F8, 28, 28) (dual of [(2340, 28), 65399, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8121, 32760, F8, 28) (dual of [32760, 32639, 29]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8121, 32760, F8, 28) (dual of [32760, 32639, 29]-code), using
- net defined by OOA [i] based on linear OOA(8121, 2340, F8, 28, 28) (dual of [(2340, 28), 65399, 29]-NRT-code), using
- digital (9, 23, 45)-net over F8, using
(144−28, 144, 4682)-Net in Base 8 — Constructive
(116, 144, 4682)-net in base 8, using
- base change [i] based on digital (80, 108, 4682)-net over F16, using
- 161 times duplication [i] based on digital (79, 107, 4682)-net over F16, using
- net defined by OOA [i] based on linear OOA(16107, 4682, F16, 28, 28) (dual of [(4682, 28), 130989, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16107, 65548, F16, 28) (dual of [65548, 65441, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] 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]
- 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]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16107, 65548, F16, 28) (dual of [65548, 65441, 29]-code), using
- net defined by OOA [i] based on linear OOA(16107, 4682, F16, 28, 28) (dual of [(4682, 28), 130989, 29]-NRT-code), using
- 161 times duplication [i] based on digital (79, 107, 4682)-net over F16, using
(144−28, 144, 102293)-Net over F8 — Digital
Digital (116, 144, 102293)-net over F8, using
(144−28, 144, large)-Net in Base 8 — Upper bound on s
There is no (116, 144, large)-net in base 8, because
- 26 times m-reduction [i] would yield (116, 118, large)-net in base 8, but