Best Known (122−28, 122, s)-Nets in Base 5
(122−28, 122, 460)-Net over F5 — Constructive and digital
Digital (94, 122, 460)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (32, 46, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 23, 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, 23, 104)-net over F25, using
- digital (48, 76, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 38, 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, 38, 126)-net over F25, using
- digital (32, 46, 208)-net over F5, using
(122−28, 122, 3948)-Net over F5 — Digital
Digital (94, 122, 3948)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5122, 3948, F5, 28) (dual of [3948, 3826, 29]-code), using
- 807 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 31 times 0, 1, 63 times 0, 1, 109 times 0, 1, 158 times 0, 1, 195 times 0, 1, 220 times 0) [i] based on linear OA(5111, 3130, F5, 28) (dual of [3130, 3019, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(5111, 3125, F5, 28) (dual of [3125, 3014, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(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(27) ⊂ Ce(26) [i] based on
- 807 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 31 times 0, 1, 63 times 0, 1, 109 times 0, 1, 158 times 0, 1, 195 times 0, 1, 220 times 0) [i] based on linear OA(5111, 3130, F5, 28) (dual of [3130, 3019, 29]-code), using
(122−28, 122, 1863887)-Net in Base 5 — Upper bound on s
There is no (94, 122, 1863888)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 18 807952 488422 054388 345570 356602 055797 844006 836995 691046 358976 278121 544017 115240 225025 > 5122 [i]