Best Known (99, 125, s)-Nets in Base 4
(99, 125, 1049)-Net over F4 — Constructive and digital
Digital (99, 125, 1049)-net over F4, using
- 41 times duplication [i] based on digital (98, 124, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence 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 (7, 20, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(99, 125, 4180)-Net over F4 — Digital
Digital (99, 125, 4180)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4125, 4180, F4, 26) (dual of [4180, 4055, 27]-code), using
- 68 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) [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
- 68 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) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
(99, 125, 1162303)-Net in Base 4 — Upper bound on s
There is no (99, 125, 1162304)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1809 267197 704530 061915 579697 895963 972755 050771 051118 846961 244732 876981 745497 > 4125 [i]