Best Known (26, 26+34, s)-Nets in Base 27
(26, 26+34, 132)-Net over F27 — Constructive and digital
Digital (26, 60, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 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 (5, 39, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 21, 64)-net over F27, using
(26, 26+34, 172)-Net in Base 27 — Constructive
(26, 60, 172)-net in base 27, using
- 16 times m-reduction [i] based on (26, 76, 172)-net in base 27, using
- base change [i] based on digital (7, 57, 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, 57, 172)-net over F81, using
(26, 26+34, 209)-Net over F27 — Digital
Digital (26, 60, 209)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2760, 209, F27, 2, 34) (dual of [(209, 2), 358, 35]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2758, 208, F27, 2, 34) (dual of [(208, 2), 358, 35]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,381P) [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2758, 208, F27, 2, 34) (dual of [(208, 2), 358, 35]-NRT-code), using
(26, 26+34, 244)-Net in Base 27
(26, 60, 244)-net in base 27, using
- 8 times m-reduction [i] based on (26, 68, 244)-net in base 27, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
(26, 26+34, 31097)-Net in Base 27 — Upper bound on s
There is no (26, 60, 31098)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 76 205147 197338 786029 733529 529076 800011 248388 170582 717505 662817 861307 770318 226478 378693 > 2760 [i]