Best Known (136, 136+36, s)-Nets in Base 4
(136, 136+36, 1056)-Net over F4 — Constructive and digital
Digital (136, 172, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 43, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(136, 136+36, 4339)-Net over F4 — Digital
Digital (136, 172, 4339)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4172, 4339, F4, 36) (dual of [4339, 4167, 37]-code), using
- 234 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, 1, 60 times 0, 1, 88 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
- 234 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, 1, 60 times 0, 1, 88 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(136, 136+36, 1425680)-Net in Base 4 — Upper bound on s
There is no (136, 172, 1425681)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 35 836334 617141 534122 061849 585014 032926 532434 391936 019452 591764 709772 724916 917506 157545 280133 133270 245392 > 4172 [i]