Best Known (26−15, 26, s)-Nets in Base 81
(26−15, 26, 232)-Net over F81 — Constructive and digital
Digital (11, 26, 232)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 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 (2, 17, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81 (see above)
- digital (2, 9, 116)-net over F81, using
(26−15, 26, 277)-Net over F81 — Digital
Digital (11, 26, 277)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8126, 277, F81, 15) (dual of [277, 251, 16]-code), using
- 48 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 40 times 0) [i] based on linear OA(8123, 226, F81, 15) (dual of [226, 203, 16]-code), using
- extended algebraic-geometric code AGe(F,210P) [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
- 48 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 40 times 0) [i] based on linear OA(8123, 226, F81, 15) (dual of [226, 203, 16]-code), using
(26−15, 26, 276593)-Net in Base 81 — Upper bound on s
There is no (11, 26, 276594)-net in base 81, because
- 1 times m-reduction [i] would yield (11, 25, 276594)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 515385 970011 202279 876936 871940 779144 788026 988641 > 8125 [i]