Best Known (85, 113, s)-Nets in Base 4
(85, 113, 1028)-Net over F4 — Constructive and digital
Digital (85, 113, 1028)-net over F4, using
- 41 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
(85, 113, 1221)-Net over F4 — Digital
Digital (85, 113, 1221)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4113, 1221, F4, 28) (dual of [1221, 1108, 29]-code), using
- 190 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) [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]
- 190 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) [i] based on linear OA(4105, 1023, F4, 28) (dual of [1023, 918, 29]-code), using
(85, 113, 145810)-Net in Base 4 — Upper bound on s
There is no (85, 113, 145811)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 107 849678 684676 839063 788860 313067 617012 350736 525209 832684 408024 506868 > 4113 [i]