Best Known (79, 79+22, s)-Nets in Base 4
(79, 79+22, 1040)-Net over F4 — Constructive and digital
Digital (79, 101, 1040)-net over F4, using
- 41 times duplication [i] based on digital (78, 100, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 25, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 25, 260)-net over F256, using
(79, 79+22, 2819)-Net over F4 — Digital
Digital (79, 101, 2819)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4101, 2819, F4, 22) (dual of [2819, 2718, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 4113, F4, 22) (dual of [4113, 4012, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [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(479, 4096, F4, 18) (dual of [4096, 4017, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-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(4101, 4113, F4, 22) (dual of [4113, 4012, 23]-code), using
(79, 79+22, 551939)-Net in Base 4 — Upper bound on s
There is no (79, 101, 551940)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6 427819 274938 692875 918397 793786 842401 594505 303708 239331 035008 > 4101 [i]