Best Known (102, 102+13, s)-Nets in Base 4
(102, 102+13, 1398105)-Net over F4 — Constructive and digital
Digital (102, 115, 1398105)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (96, 109, 1398100)-net over F4, using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- digital (0, 6, 5)-net over F4, using
(102, 102+13, 4194306)-Net over F4 — Digital
Digital (102, 115, 4194306)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4115, 4194306, F4, 2, 13) (dual of [(4194306, 2), 8388497, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(46, 5, F4, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;4,4) [i]
- linear OOA(4109, 4194301, F4, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 2-folding [i] based on linear OA(4109, 8388602, F4, 13) (dual of [8388602, 8388493, 14]-code), using
- linear OOA(46, 5, F4, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(102, 102+13, large)-Net in Base 4 — Upper bound on s
There is no (102, 115, large)-net in base 4, because
- 11 times m-reduction [i] would yield (102, 104, large)-net in base 4, but