Best Known (128−14, 128, s)-Nets in Base 4
(128−14, 128, 1198376)-Net over F4 — Constructive and digital
Digital (114, 128, 1198376)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (107, 121, 1198371)-net over F4, using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- digital (0, 7, 5)-net over F4, using
(128−14, 128, 4194306)-Net over F4 — Digital
Digital (114, 128, 4194306)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4128, 4194306, F4, 2, 14) (dual of [(4194306, 2), 8388484, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(47, 5, F4, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;3,4) [i]
- linear OOA(4121, 4194301, F4, 2, 14) (dual of [(4194301, 2), 8388481, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4121, 8388602, F4, 14) (dual of [8388602, 8388481, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OOA 2-folding [i] based on linear OA(4121, 8388602, F4, 14) (dual of [8388602, 8388481, 15]-code), using
- linear OOA(47, 5, F4, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(128−14, 128, large)-Net in Base 4 — Upper bound on s
There is no (114, 128, large)-net in base 4, because
- 12 times m-reduction [i] would yield (114, 116, large)-net in base 4, but