Best Known (192−42, 192, s)-Nets in Base 4
(192−42, 192, 1052)-Net over F4 — Constructive and digital
Digital (150, 192, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(192−42, 192, 3909)-Net over F4 — Digital
Digital (150, 192, 3909)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4192, 3909, F4, 42) (dual of [3909, 3717, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(4192, 4119, F4, 42) (dual of [4119, 3927, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(37) [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(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(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(41) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(4192, 4119, F4, 42) (dual of [4119, 3927, 43]-code), using
(192−42, 192, 924510)-Net in Base 4 — Upper bound on s
There is no (150, 192, 924511)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 39 402509 033242 792938 747762 915043 024371 292790 466487 980557 876051 551104 105686 102979 654486 565119 823789 818123 301592 537854 > 4192 [i]