Best Known (160, 202, s)-Nets in Base 4
(160, 202, 1060)-Net over F4 — Constructive and digital
Digital (160, 202, 1060)-net over F4, using
- 42 times duplication [i] based on digital (158, 200, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 50, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 50, 265)-net over F256, using
(160, 202, 4999)-Net over F4 — Digital
Digital (160, 202, 4999)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4202, 4999, F4, 42) (dual of [4999, 4797, 43]-code), using
- 882 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 19 times 0, 1, 33 times 0, 1, 52 times 0, 1, 74 times 0, 1, 99 times 0, 1, 122 times 0, 1, 139 times 0, 1, 152 times 0, 1, 161 times 0) [i] based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(40) [i] based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(41) ⊂ Ce(40) [i] based on
- 882 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 19 times 0, 1, 33 times 0, 1, 52 times 0, 1, 74 times 0, 1, 99 times 0, 1, 122 times 0, 1, 139 times 0, 1, 152 times 0, 1, 161 times 0) [i] based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
(160, 202, 1789002)-Net in Base 4 — Upper bound on s
There is no (160, 202, 1789003)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 41 316311 871424 591873 436928 305027 441384 153055 675060 627654 276417 377643 463854 130383 931536 265292 994434 525414 853057 374108 049040 > 4202 [i]