Best Known (174−38, 174, s)-Nets in Base 4
(174−38, 174, 1048)-Net over F4 — Constructive and digital
Digital (136, 174, 1048)-net over F4, using
- 42 times duplication [i] based on digital (134, 172, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 43, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 43, 262)-net over F256, using
(174−38, 174, 3694)-Net over F4 — Digital
Digital (136, 174, 3694)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4174, 3694, F4, 38) (dual of [3694, 3520, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 4119, F4, 38) (dual of [4119, 3945, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(4174, 4119, F4, 38) (dual of [4119, 3945, 39]-code), using
(174−38, 174, 862359)-Net in Base 4 — Upper bound on s
There is no (136, 174, 862360)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 573 375864 671721 523857 809245 347850 813011 863769 236766 057624 769329 045397 526034 983691 243852 693871 846378 147873 > 4174 [i]