Best Known (84, 106, s)-Nets in Base 4
(84, 106, 1049)-Net over F4 — Constructive and digital
Digital (84, 106, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (66, 88, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- digital (7, 18, 21)-net over F4, using
(84, 106, 3993)-Net over F4 — Digital
Digital (84, 106, 3993)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4106, 3993, F4, 22) (dual of [3993, 3887, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 4130, F4, 22) (dual of [4130, 4024, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(473, 4096, F4, 17) (dual of [4096, 4023, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(467, 4096, F4, 15) (dual of [4096, 4029, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(47, 32, F4, 4) (dual of [32, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(21) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4106, 4130, F4, 22) (dual of [4130, 4024, 23]-code), using
(84, 106, 1036473)-Net in Base 4 — Upper bound on s
There is no (84, 106, 1036474)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6582 040713 241180 743664 494841 289381 845992 353455 706311 890189 619048 > 4106 [i]