Best Known (10, 24, s)-Nets in Base 81
(10, 24, 216)-Net over F81 — Constructive and digital
Digital (10, 24, 216)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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, 16, 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, 8, 100)-net over F81, using
(10, 24, 257)-Net over F81 — Digital
Digital (10, 24, 257)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8124, 257, F81, 14) (dual of [257, 233, 15]-code), using
- 12 step Varšamov–Edel lengthening with (ri) = (1, 11 times 0) [i] based on linear OA(8123, 244, F81, 14) (dual of [244, 221, 15]-code), using
- extended algebraic-geometric code AGe(F,229P) [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- 12 step Varšamov–Edel lengthening with (ri) = (1, 11 times 0) [i] based on linear OA(8123, 244, F81, 14) (dual of [244, 221, 15]-code), using
(10, 24, 147637)-Net in Base 81 — Upper bound on s
There is no (10, 24, 147638)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 6362 825611 579381 209540 204693 227239 618579 707681 > 8124 [i]