Best Known (49, 62, s)-Nets in Base 4
(49, 62, 1054)-Net over F4 — Constructive and digital
Digital (49, 62, 1054)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 26)-net over F4, using
- digital (39, 52, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 13, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 13, 257)-net over F256, using
(49, 62, 3561)-Net over F4 — Digital
Digital (49, 62, 3561)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(462, 3561, F4, 13) (dual of [3561, 3499, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(462, 4105, F4, 13) (dual of [4105, 4043, 14]-code), using
- (u, u+v)-construction [i] based on
- linear OA(47, 9, F4, 6) (dual of [9, 2, 7]-code), using
- 1 times truncation [i] based on linear OA(48, 10, F4, 7) (dual of [10, 2, 8]-code), using
- repeating each code word 2 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reed–Solomon code RSe(2,4) [i]
- Simplex code S(2,4) [i]
- repeating each code word 2 times [i] based on linear OA(43, 5, F4, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- 1 times truncation [i] based on linear OA(48, 10, F4, 7) (dual of [10, 2, 8]-code), using
- linear OA(455, 4096, F4, 13) (dual of [4096, 4041, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 9, F4, 6) (dual of [9, 2, 7]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(462, 4105, F4, 13) (dual of [4105, 4043, 14]-code), using
(49, 62, 1318386)-Net in Base 4 — Upper bound on s
There is no (49, 62, 1318387)-net in base 4, because
- 1 times m-reduction [i] would yield (49, 61, 1318387)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 5 316935 574884 074813 206716 306513 933980 > 461 [i]