Best Known (30−11, 30, s)-Nets in Base 9
(30−11, 30, 300)-Net over F9 — Constructive and digital
Digital (19, 30, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 15, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(30−11, 30, 611)-Net over F9 — Digital
Digital (19, 30, 611)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(930, 611, F9, 11) (dual of [611, 581, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(930, 728, F9, 11) (dual of [728, 698, 12]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(930, 728, F9, 11) (dual of [728, 698, 12]-code), using
(30−11, 30, 111517)-Net in Base 9 — Upper bound on s
There is no (19, 30, 111518)-net in base 9, because
- 1 times m-reduction [i] would yield (19, 29, 111518)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 4710 257632 529487 766764 026673 > 929 [i]