Best Known (21, 21+11, s)-Nets in Base 4
(21, 21+11, 98)-Net over F4 — Constructive and digital
Digital (21, 32, 98)-net over F4, using
- trace code for nets [i] based on digital (5, 16, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
(21, 21+11, 158)-Net over F4 — Digital
Digital (21, 32, 158)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(432, 158, F4, 11) (dual of [158, 126, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(432, 160, F4, 11) (dual of [160, 128, 12]-code), using
(21, 21+11, 4689)-Net in Base 4 — Upper bound on s
There is no (21, 32, 4690)-net in base 4, because
- 1 times m-reduction [i] would yield (21, 31, 4690)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 4 613023 955524 745860 > 431 [i]