Best Known (18−7, 18, s)-Nets in Base 4
(18−7, 18, 66)-Net over F4 — Constructive and digital
Digital (11, 18, 66)-net over F4, using
- trace code for nets [i] based on digital (2, 9, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
(18−7, 18, 94)-Net over F4 — Digital
Digital (11, 18, 94)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(418, 94, F4, 7) (dual of [94, 76, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 108, F4, 7) (dual of [108, 90, 8]-code), using
- a “BZ†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(418, 108, F4, 7) (dual of [108, 90, 8]-code), using
(18−7, 18, 1560)-Net in Base 4 — Upper bound on s
There is no (11, 18, 1561)-net in base 4, because
- 1 times m-reduction [i] would yield (11, 17, 1561)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 17182 587304 > 417 [i]