Best Known (46, 74, s)-Nets in Base 128
(46, 74, 1386)-Net over F128 — Constructive and digital
Digital (46, 74, 1386)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (27, 55, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- digital (5, 19, 216)-net over F128, using
(46, 74, 4683)-Net in Base 128 — Constructive
(46, 74, 4683)-net in base 128, using
- 1282 times duplication [i] based on (44, 72, 4683)-net in base 128, using
- base change [i] based on digital (35, 63, 4683)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
- base change [i] based on digital (35, 63, 4683)-net over F256, using
(46, 74, 51290)-Net over F128 — Digital
Digital (46, 74, 51290)-net over F128, using
(46, 74, large)-Net in Base 128 — Upper bound on s
There is no (46, 74, large)-net in base 128, because
- 26 times m-reduction [i] would yield (46, 48, large)-net in base 128, but