Best Known (105−25, 105, s)-Nets in Base 5
(105−25, 105, 400)-Net over F5 — Constructive and digital
Digital (80, 105, 400)-net over F5, using
- 5 times m-reduction [i] based on digital (80, 110, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 55, 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, 55, 200)-net over F25, using
(105−25, 105, 3174)-Net over F5 — Digital
Digital (80, 105, 3174)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5105, 3174, F5, 25) (dual of [3174, 3069, 26]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0) [i] based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0) [i] based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
(105−25, 105, 1510215)-Net in Base 5 — Upper bound on s
There is no (80, 105, 1510216)-net in base 5, because
- 1 times m-reduction [i] would yield (80, 104, 1510216)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4 930387 675198 825508 967227 639898 777368 900835 905409 527967 700422 077860 475905 > 5104 [i]