Best Known (104, 130, s)-Nets in Base 4
(104, 130, 1062)-Net over F4 — Constructive and digital
Digital (104, 130, 1062)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 26, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 13, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- trace code for nets [i] based on digital (0, 13, 17)-net over F16, using
- digital (78, 104, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 26, 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, 26, 257)-net over F256, using
- digital (13, 26, 34)-net over F4, using
(104, 130, 4685)-Net over F4 — Digital
Digital (104, 130, 4685)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4130, 4685, F4, 26) (dual of [4685, 4555, 27]-code), using
- 568 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 26 times 0, 1, 40 times 0, 1, 62 times 0, 1, 92 times 0, 1, 129 times 0, 1, 172 times 0) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 568 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 26 times 0, 1, 40 times 0, 1, 62 times 0, 1, 92 times 0, 1, 129 times 0, 1, 172 times 0) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
(104, 130, 1980991)-Net in Base 4 — Upper bound on s
There is no (104, 130, 1980992)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 852681 764494 311850 702123 689906 362417 227365 646309 352013 963025 728204 818093 310105 > 4130 [i]