Best Known (92, 117, s)-Nets in Base 4
(92, 117, 1045)-Net over F4 — Constructive and digital
Digital (92, 117, 1045)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (75, 100, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 25, 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, 25, 257)-net over F256, using
- digital (5, 17, 17)-net over F4, using
(92, 117, 3400)-Net over F4 — Digital
Digital (92, 117, 3400)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4117, 3400, F4, 25) (dual of [3400, 3283, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4117, 4124, F4, 25) (dual of [4124, 4007, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 25, F4, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4117, 4124, F4, 25) (dual of [4124, 4007, 26]-code), using
(92, 117, 1164527)-Net in Base 4 — Upper bound on s
There is no (92, 117, 1164528)-net in base 4, because
- 1 times m-reduction [i] would yield (92, 116, 1164528)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 6901 759622 570117 158526 140594 324750 345872 863780 744667 753780 257440 725403 > 4116 [i]