Best Known (86−20, 86, s)-Nets in Base 4
(86−20, 86, 1032)-Net over F4 — Constructive and digital
Digital (66, 86, 1032)-net over F4, using
- 42 times duplication [i] based on digital (64, 84, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 21, 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, 21, 258)-net over F256, using
(86−20, 86, 1414)-Net over F4 — Digital
Digital (66, 86, 1414)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(486, 1414, F4, 20) (dual of [1414, 1328, 21]-code), using
- 380 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 4 times 0, 1, 10 times 0, 1, 20 times 0, 1, 34 times 0, 1, 52 times 0, 1, 70 times 0, 1, 84 times 0, 1, 94 times 0) [i] based on linear OA(475, 1023, F4, 20) (dual of [1023, 948, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 380 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 4 times 0, 1, 10 times 0, 1, 20 times 0, 1, 34 times 0, 1, 52 times 0, 1, 70 times 0, 1, 84 times 0, 1, 94 times 0) [i] based on linear OA(475, 1023, F4, 20) (dual of [1023, 948, 21]-code), using
(86−20, 86, 227277)-Net in Base 4 — Upper bound on s
There is no (66, 86, 227278)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5986 502708 922841 467052 259569 746217 640599 584216 233206 > 486 [i]