Best Known (82, 82+26, s)-Nets in Base 5
(82, 82+26, 400)-Net over F5 — Constructive and digital
Digital (82, 108, 400)-net over F5, using
- 6 times m-reduction [i] based on digital (82, 114, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 57, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 57, 200)-net over F25, using
(82, 82+26, 3181)-Net over F5 — Digital
Digital (82, 108, 3181)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5108, 3181, F5, 26) (dual of [3181, 3073, 27]-code), using
- 49 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 49 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(82, 82+26, 908174)-Net in Base 5 — Upper bound on s
There is no (82, 108, 908175)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3081 492593 540497 044685 913540 177554 997512 563420 210573 169911 044736 068763 406861 > 5108 [i]