Best Known (134, 134+36, s)-Nets in Base 4
(134, 134+36, 1052)-Net over F4 — Constructive and digital
Digital (134, 170, 1052)-net over F4, using
- 42 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
(134, 134+36, 4187)-Net over F4 — Digital
Digital (134, 170, 4187)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4170, 4187, F4, 36) (dual of [4187, 4017, 37]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 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
- 84 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(134, 134+36, 1222153)-Net in Base 4 — Upper bound on s
There is no (134, 170, 1222154)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 239758 089077 868951 573002 138123 942212 363345 951374 234772 831314 299268 279868 247231 580991 835208 321733 574528 > 4170 [i]