Best Known (100, 126, s)-Nets in Base 4
(100, 126, 1051)-Net over F4 — Constructive and digital
Digital (100, 126, 1051)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (9, 22, 23)-net over F4, using
- 1 times m-reduction [i] based on digital (9, 23, 23)-net over F4, 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 (9, 22, 23)-net over F4, using
(100, 126, 4222)-Net over F4 — Digital
Digital (100, 126, 4222)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4126, 4222, F4, 26) (dual of [4222, 4096, 27]-code), using
- 109 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) [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
- 109 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) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
(100, 126, 1293100)-Net in Base 4 — Upper bound on s
There is no (100, 126, 1293101)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7237 072602 485318 125166 620652 682089 798374 277223 691880 877358 451833 946056 996324 > 4126 [i]