Best Known (102, 102+28, s)-Nets in Base 4
(102, 102+28, 1044)-Net over F4 — Constructive and digital
Digital (102, 130, 1044)-net over F4, using
- 42 times duplication [i] based on digital (100, 128, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 32, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 32, 261)-net over F256, using
(102, 102+28, 3394)-Net over F4 — Digital
Digital (102, 130, 3394)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4130, 3394, F4, 28) (dual of [3394, 3264, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4130, 4117, F4, 28) (dual of [4117, 3987, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4130, 4117, F4, 28) (dual of [4117, 3987, 29]-code), using
(102, 102+28, 785032)-Net in Base 4 — Upper bound on s
There is no (102, 130, 785033)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 852705 905903 205942 465437 581361 841521 418100 250096 172582 453361 357248 381931 642560 > 4130 [i]