Best Known (171−36, 171, s)-Nets in Base 4
(171−36, 171, 1052)-Net over F4 — Constructive and digital
Digital (135, 171, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (135, 172, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 43, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 43, 263)-net over F256, using
(171−36, 171, 4249)-Net over F4 — Digital
Digital (135, 171, 4249)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4171, 4249, F4, 36) (dual of [4249, 4078, 37]-code), using
- 145 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 times 0, 1, 60 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- 145 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 times 0, 1, 60 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(171−36, 171, 1320000)-Net in Base 4 — Upper bound on s
There is no (135, 171, 1320001)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 959094 541821 967963 237783 042956 310800 422368 838570 174957 054916 819774 501124 844806 570896 522254 293561 960736 > 4171 [i]