Best Known (24−9, 24, s)-Nets in Base 4
(24−9, 24, 76)-Net over F4 — Constructive and digital
Digital (15, 24, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 12, 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
(24−9, 24, 103)-Net over F4 — Digital
Digital (15, 24, 103)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(424, 103, F4, 9) (dual of [103, 79, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(424, 144, F4, 9) (dual of [144, 120, 10]-code), using
(24−9, 24, 2134)-Net in Base 4 — Upper bound on s
There is no (15, 24, 2135)-net in base 4, because
- 1 times m-reduction [i] would yield (15, 23, 2135)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 70 496556 523891 > 423 [i]