Best Known (100−24, 100, s)-Nets in Base 4
(100−24, 100, 1032)-Net over F4 — Constructive and digital
Digital (76, 100, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 25, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
(100−24, 100, 1316)-Net over F4 — Digital
Digital (76, 100, 1316)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4100, 1316, F4, 24) (dual of [1316, 1216, 25]-code), using
- 282 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 7 times 0, 1, 13 times 0, 1, 24 times 0, 1, 38 times 0, 1, 52 times 0, 1, 64 times 0, 1, 72 times 0) [i] based on linear OA(490, 1024, F4, 24) (dual of [1024, 934, 25]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(491, 1025, F4, 25) (dual of [1025, 934, 26]-code), using
- 282 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 7 times 0, 1, 13 times 0, 1, 24 times 0, 1, 38 times 0, 1, 52 times 0, 1, 64 times 0, 1, 72 times 0) [i] based on linear OA(490, 1024, F4, 24) (dual of [1024, 934, 25]-code), using
(100−24, 100, 183393)-Net in Base 4 — Upper bound on s
There is no (76, 100, 183394)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 606976 474447 036015 599811 859920 681394 629091 845946 029608 644280 > 4100 [i]