Best Known (36−21, 36, s)-Nets in Base 27
(36−21, 36, 102)-Net over F27 — Constructive and digital
Digital (15, 36, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (4, 25, 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 (1, 11, 38)-net over F27, using
(36−21, 36, 137)-Net over F27 — Digital
Digital (15, 36, 137)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2736, 137, F27, 2, 21) (dual of [(137, 2), 238, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2734, 136, F27, 2, 21) (dual of [(136, 2), 238, 22]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,250P) [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2734, 136, F27, 2, 21) (dual of [(136, 2), 238, 22]-NRT-code), using
(36−21, 36, 160)-Net in Base 27 — Constructive
(15, 36, 160)-net in base 27, using
- 4 times m-reduction [i] based on (15, 40, 160)-net in base 27, using
- base change [i] based on digital (5, 30, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 30, 160)-net over F81, using
(36−21, 36, 190)-Net in Base 27
(15, 36, 190)-net in base 27, using
- base change [i] based on digital (6, 27, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(36−21, 36, 17809)-Net in Base 27 — Upper bound on s
There is no (15, 36, 17810)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 35, 17810)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 125 256566 881170 770268 086273 867665 704878 005946 488453 > 2735 [i]