Best Known (28−17, 28, s)-Nets in Base 81
(28−17, 28, 216)-Net over F81 — Constructive and digital
Digital (11, 28, 216)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (2, 19, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (1, 9, 100)-net over F81, using
(28−17, 28, 245)-Net over F81 — Digital
Digital (11, 28, 245)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8128, 245, F81, 2, 17) (dual of [(245, 2), 462, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8126, 244, F81, 2, 17) (dual of [(244, 2), 462, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,470P) [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8126, 244, F81, 2, 17) (dual of [(244, 2), 462, 18]-NRT-code), using
(28−17, 28, 129934)-Net in Base 81 — Upper bound on s
There is no (11, 28, 129935)-net in base 81, because
- 1 times m-reduction [i] would yield (11, 27, 129935)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3381 464541 401362 026765 042140 039478 045712 652728 534401 > 8127 [i]