Best Known (80, 105, s)-Nets in Base 4
(80, 105, 1032)-Net over F4 — Constructive and digital
Digital (80, 105, 1032)-net over F4, using
- 41 times duplication [i] based on digital (79, 104, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 26, 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, 26, 258)-net over F256, using
(80, 105, 1420)-Net over F4 — Digital
Digital (80, 105, 1420)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4105, 1420, F4, 25) (dual of [1420, 1315, 26]-code), using
- 381 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 29 times 0, 1, 40 times 0, 1, 51 times 0, 1, 61 times 0, 1, 69 times 0, 1, 75 times 0) [i] based on linear OA(491, 1025, F4, 25) (dual of [1025, 934, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 381 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 29 times 0, 1, 40 times 0, 1, 51 times 0, 1, 61 times 0, 1, 69 times 0, 1, 75 times 0) [i] based on linear OA(491, 1025, F4, 25) (dual of [1025, 934, 26]-code), using
(80, 105, 291124)-Net in Base 4 — Upper bound on s
There is no (80, 105, 291125)-net in base 4, because
- 1 times m-reduction [i] would yield (80, 104, 291125)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 411 379048 227384 774918 832824 933179 288939 427225 087797 448153 971926 > 4104 [i]