Best Known (93−22, 93, s)-Nets in Base 5
(93−22, 93, 356)-Net over F5 — Constructive and digital
Digital (71, 93, 356)-net over F5, using
- 1 times m-reduction [i] based on digital (71, 94, 356)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (17, 28, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 14, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- trace code for nets [i] based on digital (3, 14, 52)-net over F25, using
- digital (43, 66, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 33, 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, 33, 126)-net over F25, using
- digital (17, 28, 104)-net over F5, using
- (u, u+v)-construction [i] based on
(93−22, 93, 3207)-Net over F5 — Digital
Digital (71, 93, 3207)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(593, 3207, F5, 22) (dual of [3207, 3114, 23]-code), using
- 70 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0, 1, 35 times 0) [i] based on linear OA(586, 3130, F5, 22) (dual of [3130, 3044, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(586, 3125, F5, 22) (dual of [3125, 3039, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(581, 3125, F5, 21) (dual of [3125, 3044, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- 70 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0, 1, 35 times 0) [i] based on linear OA(586, 3130, F5, 22) (dual of [3130, 3044, 23]-code), using
(93−22, 93, 996378)-Net in Base 5 — Upper bound on s
There is no (71, 93, 996379)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 100974 466310 989918 465041 766770 911982 070691 478309 990834 719379 470725 > 593 [i]