Best Known (14, 20, s)-Nets in Base 4
(14, 20, 195)-Net over F4 — Constructive and digital
Digital (14, 20, 195)-net over F4, using
- 1 times m-reduction [i] based on digital (14, 21, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
(14, 20, 346)-Net over F4 — Digital
Digital (14, 20, 346)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(420, 346, F4, 6) (dual of [346, 326, 7]-code), using
- construction X applied to C([110,115]) ⊂ C([111,115]) [i] based on
- linear OA(420, 341, F4, 6) (dual of [341, 321, 7]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {110,111,…,115}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(415, 341, F4, 5) (dual of [341, 326, 6]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {111,112,113,114,115}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to C([110,115]) ⊂ C([111,115]) [i] based on
(14, 20, 6249)-Net in Base 4 — Upper bound on s
There is no (14, 20, 6250)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 099687 696876 > 420 [i]