Best Known (85, 110, s)-Nets in Base 5
(85, 110, 416)-Net over F5 — Constructive and digital
Digital (85, 110, 416)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (30, 42, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 21, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 21, 104)-net over F25, using
- digital (43, 68, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 34, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- trace code for nets [i] based on digital (9, 34, 104)-net over F25, using
- digital (30, 42, 208)-net over F5, using
(85, 110, 3933)-Net over F5 — Digital
Digital (85, 110, 3933)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5110, 3933, F5, 25) (dual of [3933, 3823, 26]-code), using
- 799 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0, 1, 52 times 0, 1, 97 times 0, 1, 154 times 0, 1, 205 times 0, 1, 241 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
- 799 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0, 1, 52 times 0, 1, 97 times 0, 1, 154 times 0, 1, 205 times 0, 1, 241 times 0) [i] based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
(85, 110, 2953096)-Net in Base 5 — Upper bound on s
There is no (85, 110, 2953097)-net in base 5, because
- 1 times m-reduction [i] would yield (85, 109, 2953097)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 15407 439863 822398 511756 544632 752952 230510 668270 995432 795068 632552 641581 752145 > 5109 [i]