Best Known (10, 10+11, s)-Nets in Base 4
(10, 10+11, 28)-Net over F4 — Constructive and digital
Digital (10, 21, 28)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 16)-net over F4, using
- digital (3, 14, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
(10, 10+11, 29)-Net over F4 — Digital
Digital (10, 21, 29)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(421, 29, F4, 2, 11) (dual of [(29, 2), 37, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(421, 32, F4, 2, 11) (dual of [(32, 2), 43, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(421, 64, F4, 11) (dual of [64, 43, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 65, F4, 11) (dual of [65, 44, 12]-code), using
- OOA 2-folding [i] based on linear OA(421, 64, F4, 11) (dual of [64, 43, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(421, 32, F4, 2, 11) (dual of [(32, 2), 43, 12]-NRT-code), using
(10, 10+11, 218)-Net in Base 4 — Upper bound on s
There is no (10, 21, 219)-net in base 4, because
- 1 times m-reduction [i] would yield (10, 20, 219)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 107806 785588 > 420 [i]