Best Known (40, 52, s)-Nets in Base 4
(40, 52, 1032)-Net over F4 — Constructive and digital
Digital (40, 52, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 13, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
(40, 52, 1216)-Net over F4 — Digital
Digital (40, 52, 1216)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(452, 1216, F4, 12) (dual of [1216, 1164, 13]-code), using
- 186 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 27 times 0, 1, 50 times 0, 1, 82 times 0) [i] based on linear OA(445, 1023, F4, 12) (dual of [1023, 978, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 186 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 27 times 0, 1, 50 times 0, 1, 82 times 0) [i] based on linear OA(445, 1023, F4, 12) (dual of [1023, 978, 13]-code), using
(40, 52, 164794)-Net in Base 4 — Upper bound on s
There is no (40, 52, 164795)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 20 282914 942190 778204 326909 217358 > 452 [i]