Best Known (71−40, 71, s)-Nets in Base 81
(71−40, 71, 370)-Net over F81 — Constructive and digital
Digital (31, 71, 370)-net over F81, using
- t-expansion [i] based on digital (16, 71, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(71−40, 71, 594)-Net over F81 — Digital
Digital (31, 71, 594)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8171, 594, F81, 40) (dual of [594, 523, 41]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 27 times 0, 1, 53 times 0) [i] based on linear OA(8166, 500, F81, 40) (dual of [500, 434, 41]-code), using
- extended algebraic-geometric code AGe(F,459P) [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
- 89 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 27 times 0, 1, 53 times 0) [i] based on linear OA(8166, 500, F81, 40) (dual of [500, 434, 41]-code), using
(71−40, 71, 618487)-Net in Base 81 — Upper bound on s
There is no (31, 71, 618488)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3180 076766 867123 197877 476988 152044 902554 944877 770814 887464 833750 482270 991749 717326 787504 495739 901921 900971 250935 746515 860847 640157 836801 > 8171 [i]