Best Known (122, 171, s)-Nets in Base 8
(122, 171, 1026)-Net over F8 — Constructive and digital
Digital (122, 171, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 171, 1026)-net over F8, using
- 1 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
- 1 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(122, 171, 4440)-Net over F8 — Digital
Digital (122, 171, 4440)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8171, 4440, F8, 49) (dual of [4440, 4269, 50]-code), using
- 341 step Varšamov–Edel lengthening with (ri) = (1, 157 times 0, 1, 182 times 0) [i] based on linear OA(8169, 4097, F8, 49) (dual of [4097, 3928, 50]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- 341 step Varšamov–Edel lengthening with (ri) = (1, 157 times 0, 1, 182 times 0) [i] based on linear OA(8169, 4097, F8, 49) (dual of [4097, 3928, 50]-code), using
(122, 171, 3492611)-Net in Base 8 — Upper bound on s
There is no (122, 171, 3492612)-net in base 8, because
- 1 times m-reduction [i] would yield (122, 170, 3492612)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3351 969401 957807 720123 252680 104688 649186 601219 091296 309914 189309 814765 701230 655582 438641 151398 346111 874319 791647 407168 917946 650803 583681 807904 196193 717088 > 8170 [i]