Best Known (35, 35+25, s)-Nets in Base 27
(35, 35+25, 210)-Net over F27 — Constructive and digital
Digital (35, 60, 210)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 12, 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, 16, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 32, 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 (4, 12, 64)-net over F27, using
(35, 35+25, 370)-Net in Base 27 — Constructive
(35, 60, 370)-net in base 27, using
- 16 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 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, 57, 370)-net over F81, using
(35, 35+25, 1440)-Net over F27 — Digital
Digital (35, 60, 1440)-net over F27, using
(35, 35+25, 2217815)-Net in Base 27 — Upper bound on s
There is no (35, 60, 2217816)-net in base 27, because
- 1 times m-reduction [i] would yield (35, 59, 2217816)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2 821391 591169 742920 917334 839967 688227 785589 517920 306546 918088 406047 484169 934374 269121 > 2759 [i]