Best Known (27−16, 27, s)-Nets in Base 81
(27−16, 27, 216)-Net over F81 — Constructive and digital
Digital (11, 27, 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, 18, 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
(27−16, 27, 256)-Net over F81 — Digital
Digital (11, 27, 256)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8127, 256, F81, 16) (dual of [256, 229, 17]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (2, 9 times 0) [i] based on linear OA(8125, 244, F81, 16) (dual of [244, 219, 17]-code), using
- extended algebraic-geometric code AGe(F,227P) [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- 10 step Varšamov–Edel lengthening with (ri) = (2, 9 times 0) [i] based on linear OA(8125, 244, F81, 16) (dual of [244, 219, 17]-code), using
(27−16, 27, 129934)-Net in Base 81 — Upper bound on s
There is no (11, 27, 129935)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3381 464541 401362 026765 042140 039478 045712 652728 534401 > 8127 [i]