Best Known (101, 101+32, s)-Nets in Base 5
(101, 101+32, 416)-Net over F5 — Constructive and digital
Digital (101, 133, 416)-net over F5, using
- 1 times m-reduction [i] based on digital (101, 134, 416)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (34, 50, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 25, 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, 25, 104)-net over F25, using
- digital (51, 84, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 42, 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, 42, 104)-net over F25, using
- digital (34, 50, 208)-net over F5, using
- (u, u+v)-construction [i] based on
(101, 101+32, 3240)-Net over F5 — Digital
Digital (101, 133, 3240)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5133, 3240, F5, 32) (dual of [3240, 3107, 33]-code), using
- 103 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 12 times 0, 1, 27 times 0, 1, 53 times 0) [i] based on linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(31) ⊂ Ce(30) [i] based on
- 103 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 12 times 0, 1, 27 times 0, 1, 53 times 0) [i] based on linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using
(101, 101+32, 1098151)-Net in Base 5 — Upper bound on s
There is no (101, 133, 1098152)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 918 358699 826466 763136 331850 518217 322791 011767 387960 428018 207044 608702 155979 314978 429489 424385 > 5133 [i]