Best Known (108−38, 108, s)-Nets in Base 27
(108−38, 108, 517)-Net over F27 — Constructive and digital
Digital (70, 108, 517)-net over F27, using
- net defined by OOA [i] based on linear OOA(27108, 517, F27, 38, 38) (dual of [(517, 38), 19538, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(27108, 9823, F27, 38) (dual of [9823, 9715, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(27108, 9841, F27, 38) (dual of [9841, 9733, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(27108, 9823, F27, 38) (dual of [9823, 9715, 39]-code), using
(108−38, 108, 730)-Net in Base 27 — Constructive
(70, 108, 730)-net in base 27, using
- t-expansion [i] based on (63, 108, 730)-net in base 27, using
- base change [i] based on digital (36, 81, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- base change [i] based on digital (36, 81, 730)-net over F81, using
(108−38, 108, 9841)-Net over F27 — Digital
Digital (70, 108, 9841)-net over F27, using
(108−38, 108, large)-Net in Base 27 — Upper bound on s
There is no (70, 108, large)-net in base 27, because
- 36 times m-reduction [i] would yield (70, 72, large)-net in base 27, but