Best Known (86, 86+28, s)-Nets in Base 4
(86, 86+28, 1028)-Net over F4 — Constructive and digital
Digital (86, 114, 1028)-net over F4, using
- 42 times duplication [i] based on 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
(86, 86+28, 1283)-Net over F4 — Digital
Digital (86, 114, 1283)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4114, 1283, F4, 28) (dual of [1283, 1169, 29]-code), using
- 251 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 24 times 0, 1, 36 times 0, 1, 47 times 0, 1, 55 times 0, 1, 60 times 0) [i] based on linear OA(4105, 1023, F4, 28) (dual of [1023, 918, 29]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 251 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 24 times 0, 1, 36 times 0, 1, 47 times 0, 1, 55 times 0, 1, 60 times 0) [i] based on linear OA(4105, 1023, F4, 28) (dual of [1023, 918, 29]-code), using
(86, 86+28, 160988)-Net in Base 4 — Upper bound on s
There is no (86, 114, 160989)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 431 377770 142412 296412 197875 140168 134090 849666 711220 493389 149427 275432 > 4114 [i]