Best Known (20, 33, s)-Nets in Base 4
(20, 33, 76)-Net over F4 — Constructive and digital
Digital (20, 33, 76)-net over F4, using
- 1 times m-reduction [i] based on digital (20, 34, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 17, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- trace code for nets [i] based on digital (3, 17, 38)-net over F16, using
(20, 33, 86)-Net over F4 — Digital
Digital (20, 33, 86)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(433, 86, F4, 13) (dual of [86, 53, 14]-code), using
- an extension Ce(12) of the narrow-sense BCH-code C(I) with length 85 | 44−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
(20, 33, 1617)-Net in Base 4 — Upper bound on s
There is no (20, 33, 1618)-net in base 4, because
- 1 times m-reduction [i] would yield (20, 32, 1618)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 18 471205 125119 975320 > 432 [i]