Best Known (63−32, 63, s)-Nets in Base 27
(63−32, 63, 166)-Net over F27 — Constructive and digital
Digital (31, 63, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (8, 40, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 23, 82)-net over F27, using
(63−32, 63, 224)-Net in Base 27 — Constructive
(31, 63, 224)-net in base 27, using
- 9 times m-reduction [i] based on (31, 72, 224)-net in base 27, using
- base change [i] based on digital (13, 54, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 54, 224)-net over F81, using
(63−32, 63, 408)-Net over F27 — Digital
Digital (31, 63, 408)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2763, 408, F27, 32) (dual of [408, 345, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2763, 728, F27, 32) (dual of [728, 665, 33]-code), using
(63−32, 63, 113117)-Net in Base 27 — Upper bound on s
There is no (31, 63, 113118)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 499546 553645 090994 064092 745364 885937 006874 973013 848309 030765 506165 603117 345721 987618 094497 > 2763 [i]