Best Known (156, 197, s)-Nets in Base 4
(156, 197, 1060)-Net over F4 — Constructive and digital
Digital (156, 197, 1060)-net over F4, using
- 41 times duplication [i] based on digital (155, 196, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 49, 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, 49, 265)-net over F256, using
(156, 197, 4875)-Net over F4 — Digital
Digital (156, 197, 4875)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4197, 4875, F4, 41) (dual of [4875, 4678, 42]-code), using
- 762 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0, 1, 54 times 0, 1, 76 times 0, 1, 101 times 0, 1, 125 times 0, 1, 143 times 0, 1, 157 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 762 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0, 1, 37 times 0, 1, 54 times 0, 1, 76 times 0, 1, 101 times 0, 1, 125 times 0, 1, 143 times 0, 1, 157 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(156, 197, 2199731)-Net in Base 4 — Upper bound on s
There is no (156, 197, 2199732)-net in base 4, because
- 1 times m-reduction [i] would yield (156, 196, 2199732)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10086 947622 413124 815516 914633 932969 430554 278967 643625 785763 046493 506659 738643 524811 031178 807902 175614 460001 263923 768744 > 4196 [i]