Best Known (88, 112, s)-Nets in Base 4
(88, 112, 1044)-Net over F4 — Constructive and digital
Digital (88, 112, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 28, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(88, 112, 3274)-Net over F4 — Digital
Digital (88, 112, 3274)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4112, 3274, F4, 24) (dual of [3274, 3162, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4112, 4117, F4, 24) (dual of [4117, 4005, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- 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(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(24) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4112, 4117, F4, 24) (dual of [4117, 4005, 25]-code), using
(88, 112, 733603)-Net in Base 4 — Upper bound on s
There is no (88, 112, 733604)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 26 960371 235495 445982 380775 666540 618638 676461 337839 836725 273108 294840 > 4112 [i]