Best Known (169−36, 169, s)-Nets in Base 4
(169−36, 169, 1052)-Net over F4 — Constructive and digital
Digital (133, 169, 1052)-net over F4, using
- 41 times duplication [i] based on digital (132, 168, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 42, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 42, 263)-net over F256, using
(169−36, 169, 4147)-Net over F4 — Digital
Digital (133, 169, 4147)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4169, 4147, F4, 36) (dual of [4147, 3978, 37]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(169−36, 169, 1131560)-Net in Base 4 — Upper bound on s
There is no (133, 169, 1131561)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 559944 792423 079695 003203 725671 343745 941303 476682 050250 494403 238904 740623 354514 798543 919937 126586 210440 > 4169 [i]