Best Known (55, 71, s)-Nets in Base 4
(55, 71, 1032)-Net over F4 — Constructive and digital
Digital (55, 71, 1032)-net over F4, using
- 1 times m-reduction [i] based on digital (55, 72, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
(55, 71, 1525)-Net over F4 — Digital
Digital (55, 71, 1525)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(471, 1525, F4, 16) (dual of [1525, 1454, 17]-code), using
- 490 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 24 times 0, 1, 42 times 0, 1, 65 times 0, 1, 90 times 0, 1, 111 times 0, 1, 128 times 0) [i] based on linear OA(460, 1024, F4, 16) (dual of [1024, 964, 17]-code), using
- 1 times truncation [i] based on linear OA(461, 1025, F4, 17) (dual of [1025, 964, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(461, 1025, F4, 17) (dual of [1025, 964, 18]-code), using
- 490 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 24 times 0, 1, 42 times 0, 1, 65 times 0, 1, 90 times 0, 1, 111 times 0, 1, 128 times 0) [i] based on linear OA(460, 1024, F4, 16) (dual of [1024, 964, 17]-code), using
(55, 71, 276593)-Net in Base 4 — Upper bound on s
There is no (55, 71, 276594)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5 575309 912089 251397 576383 108875 418360 056906 > 471 [i]