Best Known (33, 33+51, s)-Nets in Base 27
(33, 33+51, 128)-Net over F27 — Constructive and digital
Digital (33, 84, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 29, 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, 55, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 29, 64)-net over F27, using
(33, 33+51, 172)-Net in Base 27 — Constructive
(33, 84, 172)-net in base 27, using
- 20 times m-reduction [i] based on (33, 104, 172)-net in base 27, using
- base change [i] based on digital (7, 78, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 78, 172)-net over F81, using
(33, 33+51, 220)-Net over F27 — Digital
Digital (33, 84, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
(33, 33+51, 298)-Net in Base 27
(33, 84, 298)-net in base 27, using
- base change [i] based on digital (12, 63, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(33, 33+51, 22106)-Net in Base 27 — Upper bound on s
There is no (33, 84, 22107)-net in base 27, because
- 1 times m-reduction [i] would yield (33, 83, 22107)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 63576 463334 185817 776531 423474 254367 002465 498713 108250 062215 822095 763704 715721 904777 083109 149065 282625 117331 056573 592591 > 2783 [i]