Best Known (36, 36+23, s)-Nets in Base 27
(36, 36+23, 240)-Net over F27 — Constructive and digital
Digital (36, 59, 240)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 7, 56)-net over F27, using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- digital (3, 10, 56)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 27, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (2, 7, 56)-net over F27, using
(36, 36+23, 370)-Net in Base 27 — Constructive
(36, 59, 370)-net in base 27, using
- 21 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- base change [i] based on digital (16, 60, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 60, 370)-net over F81, using
(36, 36+23, 2413)-Net over F27 — Digital
Digital (36, 59, 2413)-net over F27, using
(36, 36+23, 6656274)-Net in Base 27 — Upper bound on s
There is no (36, 59, 6656275)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 58, 6656275)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 104495 796527 216471 561181 514957 656868 019457 079723 213940 978859 448824 395731 241443 118451 > 2758 [i]