Best Known (44−17, 44, s)-Nets in Base 128
(44−17, 44, 2240)-Net over F128 — Constructive and digital
Digital (27, 44, 2240)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-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 (3, 11, 192)-net over F128, using
(44−17, 44, 8194)-Net in Base 128 — Constructive
(27, 44, 8194)-net in base 128, using
- net defined by OOA [i] based on OOA(12844, 8194, S128, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12844, 65553, S128, 17), using
- discarding factors based on OA(12844, 65554, S128, 17), using
- discarding parts of the base [i] based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- discarding parts of the base [i] based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- discarding factors based on OA(12844, 65554, S128, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12844, 65553, S128, 17), using
(44−17, 44, 33394)-Net over F128 — Digital
Digital (27, 44, 33394)-net over F128, using
(44−17, 44, large)-Net in Base 128 — Upper bound on s
There is no (27, 44, large)-net in base 128, because
- 15 times m-reduction [i] would yield (27, 29, large)-net in base 128, but