Best Known (112−26, 112, s)-Nets in Base 5
(112−26, 112, 408)-Net over F5 — Constructive and digital
Digital (86, 112, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 56, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
(112−26, 112, 3532)-Net over F5 — Digital
Digital (86, 112, 3532)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5112, 3532, F5, 26) (dual of [3532, 3420, 27]-code), using
- 396 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 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]
- 396 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(112−26, 112, 1490180)-Net in Base 5 — Upper bound on s
There is no (86, 112, 1490181)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 925936 213260 318352 020070 113791 691410 868008 388420 945476 716842 767779 851539 893925 > 5112 [i]