Best Known (48, 48+12, s)-Nets in Base 4
(48, 48+12, 1062)-Net over F4 — Constructive and digital
Digital (48, 60, 1062)-net over F4, using
- 41 times duplication [i] based on digital (47, 59, 1062)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 11, 34)-net over F4, using
- digital (36, 48, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- (u, u+v)-construction [i] based on
(48, 48+12, 4215)-Net over F4 — Digital
Digital (48, 60, 4215)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(460, 4215, F4, 12) (dual of [4215, 4155, 13]-code), using
- 114 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0, 1, 59 times 0) [i] based on linear OA(454, 4095, F4, 12) (dual of [4095, 4041, 13]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(455, 4096, F4, 13) (dual of [4096, 4041, 14]-code), using
- 114 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0, 1, 59 times 0) [i] based on linear OA(454, 4095, F4, 12) (dual of [4095, 4041, 13]-code), using
(48, 48+12, 1046402)-Net in Base 4 — Upper bound on s
There is no (48, 60, 1046403)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 329229 877048 035038 288013 066482 250720 > 460 [i]