Best Known (160−34, 160, s)-Nets in Base 4
(160−34, 160, 1052)-Net over F4 — Constructive and digital
Digital (126, 160, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 40, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(160−34, 160, 4155)-Net over F4 — Digital
Digital (126, 160, 4155)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4160, 4155, F4, 34) (dual of [4155, 3995, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4160, 4165, F4, 34) (dual of [4165, 4005, 35]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 13 times 0, 1, 20 times 0) [i] based on linear OA(4151, 4102, F4, 34) (dual of [4102, 3951, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(33) ⊂ Ce(32) [i] based on
- 54 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 13 times 0, 1, 20 times 0) [i] based on linear OA(4151, 4102, F4, 34) (dual of [4102, 3951, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4160, 4165, F4, 34) (dual of [4165, 4005, 35]-code), using
(160−34, 160, 1109853)-Net in Base 4 — Upper bound on s
There is no (126, 160, 1109854)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 136009 624946 449783 731757 587455 547078 547280 174365 617034 850292 455903 512849 290137 996333 671124 752085 > 4160 [i]