Best Known (26, 26+17, s)-Nets in Base 128
(26, 26+17, 2198)-Net over F128 — Constructive and digital
Digital (26, 43, 2198)-net over F128, using
- 1281 times duplication [i] based on digital (25, 42, 2198)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (16, 33, 2048)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 2048, F128, 17, 17) (dual of [(2048, 17), 34783, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using
- net defined by OOA [i] based on linear OOA(12833, 2048, F128, 17, 17) (dual of [(2048, 17), 34783, 18]-NRT-code), using
- digital (1, 9, 150)-net over F128, using
- (u, u+v)-construction [i] based on
(26, 26+17, 8193)-Net in Base 128 — Constructive
(26, 43, 8193)-net in base 128, using
- 1282 times duplication [i] based on (24, 41, 8193)-net in base 128, using
- net defined by OOA [i] based on OOA(12841, 8193, S128, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12841, 65545, S128, 17), using
- 1 times code embedding in larger space [i] based on OA(12840, 65544, S128, 17), using
- discarding parts of the base [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- 1 times code embedding in larger space [i] based on OA(12840, 65544, S128, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12841, 65545, S128, 17), using
- net defined by OOA [i] based on OOA(12841, 8193, S128, 17, 17), using
(26, 26+17, 24661)-Net over F128 — Digital
Digital (26, 43, 24661)-net over F128, using
(26, 26+17, large)-Net in Base 128 — Upper bound on s
There is no (26, 43, large)-net in base 128, because
- 15 times m-reduction [i] would yield (26, 28, large)-net in base 128, but