Best Known (45, 67, s)-Nets in Base 4
(45, 67, 195)-Net over F4 — Constructive and digital
Digital (45, 67, 195)-net over F4, using
- 41 times duplication [i] based on digital (44, 66, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 22, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 22, 65)-net over F64, using
(45, 67, 255)-Net over F4 — Digital
Digital (45, 67, 255)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(467, 255, F4, 22) (dual of [255, 188, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(467, 272, F4, 22) (dual of [272, 205, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(463, 256, F4, 22) (dual of [256, 193, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(451, 256, F4, 18) (dual of [256, 205, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(467, 272, F4, 22) (dual of [272, 205, 23]-code), using
(45, 67, 7594)-Net in Base 4 — Upper bound on s
There is no (45, 67, 7595)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 21798 641044 491814 029745 923583 745888 009500 > 467 [i]