Best Known (106, 134, s)-Nets in Base 4
(106, 134, 1049)-Net over F4 — Constructive and digital
Digital (106, 134, 1049)-net over F4, using
- 41 times duplication [i] based on digital (105, 133, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 21, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (84, 112, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- digital (7, 21, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(106, 134, 4164)-Net over F4 — Digital
Digital (106, 134, 4164)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4134, 4164, F4, 28) (dual of [4164, 4030, 29]-code), using
- 61 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 15 times 0, 1, 25 times 0) [i] based on linear OA(4126, 4095, F4, 28) (dual of [4095, 3969, 29]-code), using
- 1 times truncation [i] based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 1 times truncation [i] based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
- 61 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 15 times 0, 1, 25 times 0) [i] based on linear OA(4126, 4095, F4, 28) (dual of [4095, 3969, 29]-code), using
(106, 134, 1166558)-Net in Base 4 — Upper bound on s
There is no (106, 134, 1166559)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 474 287124 297340 114017 749054 194780 855367 716630 155221 296500 137352 072675 195948 029395 > 4134 [i]