Best Known (181, 230, s)-Nets in Base 4
(181, 230, 1060)-Net over F4 — Constructive and digital
Digital (181, 230, 1060)-net over F4, using
- 42 times duplication [i] based on digital (179, 228, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 57, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 57, 265)-net over F256, using
(181, 230, 4817)-Net over F4 — Digital
Digital (181, 230, 4817)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4230, 4817, F4, 49) (dual of [4817, 4587, 50]-code), using
- 707 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 34 times 0, 1, 58 times 0, 1, 83 times 0, 1, 105 times 0, 1, 120 times 0, 1, 128 times 0, 1, 134 times 0) [i] based on linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- 707 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 34 times 0, 1, 58 times 0, 1, 83 times 0, 1, 105 times 0, 1, 120 times 0, 1, 128 times 0, 1, 134 times 0) [i] based on linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using
(181, 230, 1815066)-Net in Base 4 — Upper bound on s
There is no (181, 230, 1815067)-net in base 4, because
- 1 times m-reduction [i] would yield (181, 229, 1815067)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 744286 741184 804078 332120 668156 613160 477546 666971 104873 169231 833644 369979 656456 308527 726243 783758 638967 240941 355149 156596 831649 579450 185541 > 4229 [i]