Best Known (145, 145+34, s)-Nets in Base 4
(145, 145+34, 1118)-Net over F4 — Constructive and digital
Digital (145, 179, 1118)-net over F4, using
- 41 times duplication [i] based on digital (144, 178, 1118)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (25, 42, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 21, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- trace code for nets [i] based on digital (4, 21, 45)-net over F16, using
- digital (102, 136, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 34, 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, 34, 257)-net over F256, using
- digital (25, 42, 90)-net over F4, using
- (u, u+v)-construction [i] based on
(145, 145+34, 9496)-Net over F4 — Digital
Digital (145, 179, 9496)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4179, 9496, F4, 34) (dual of [9496, 9317, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4179, 16401, F4, 34) (dual of [16401, 16222, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(4179, 16401, F4, 34) (dual of [16401, 16222, 35]-code), using
(145, 145+34, 5225891)-Net in Base 4 — Upper bound on s
There is no (145, 179, 5225892)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 587136 982539 073717 813890 696473 080000 858477 941809 153086 048210 206740 436805 773315 073217 144647 104660 619615 211590 > 4179 [i]