Best Known (91, 118, s)-Nets in Base 5
(91, 118, 460)-Net over F5 — Constructive and digital
Digital (91, 118, 460)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (31, 44, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 22, 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, 22, 104)-net over F25, using
- digital (47, 74, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- digital (31, 44, 208)-net over F5, using
(91, 118, 3943)-Net over F5 — Digital
Digital (91, 118, 3943)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5118, 3943, F5, 27) (dual of [3943, 3825, 28]-code), using
- 801 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0, 1, 37 times 0, 1, 66 times 0, 1, 104 times 0, 1, 147 times 0, 1, 188 times 0, 1, 219 times 0) [i] based on linear OA(5106, 3130, F5, 27) (dual of [3130, 3024, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- 801 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0, 1, 37 times 0, 1, 66 times 0, 1, 104 times 0, 1, 147 times 0, 1, 188 times 0, 1, 219 times 0) [i] based on linear OA(5106, 3130, F5, 27) (dual of [3130, 3024, 28]-code), using
(91, 118, 2767418)-Net in Base 5 — Upper bound on s
There is no (91, 118, 2767419)-net in base 5, because
- 1 times m-reduction [i] would yield (91, 117, 2767419)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 6018 557025 344068 241716 105872 017927 603198 995055 370368 284835 207614 529677 065555 663037 > 5117 [i]