Best Known (177−36, 177, s)-Nets in Base 4
(177−36, 177, 1061)-Net over F4 — Constructive and digital
Digital (141, 177, 1061)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 33, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (108, 144, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 36, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 36, 257)-net over F256, using
- digital (15, 33, 33)-net over F4, using
(177−36, 177, 5158)-Net over F4 — Digital
Digital (141, 177, 5158)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4177, 5158, F4, 36) (dual of [5158, 4981, 37]-code), using
- 1048 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, 1, 118 times 0, 1, 145 times 0, 1, 168 times 0, 1, 183 times 0, 1, 195 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
- 1048 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, 1, 118 times 0, 1, 145 times 0, 1, 168 times 0, 1, 183 times 0, 1, 195 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(177−36, 177, 2095377)-Net in Base 4 — Upper bound on s
There is no (141, 177, 2095378)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 36695 980523 687253 803842 270858 822978 061872 278571 933817 348652 650336 667260 169197 114194 018641 125309 166033 572200 > 4177 [i]