Best Known (93, 120, s)-Nets in Base 5
(93, 120, 504)-Net over F5 — Constructive and digital
Digital (93, 120, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (33, 46, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 23, 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, 23, 126)-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 (see above)
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- digital (33, 46, 252)-net over F5, using
(93, 120, 4452)-Net over F5 — Digital
Digital (93, 120, 4452)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5120, 4452, F5, 27) (dual of [4452, 4332, 28]-code), using
- 1308 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, 1, 243 times 0, 1, 262 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
- 1308 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, 1, 243 times 0, 1, 262 times 0) [i] based on linear OA(5106, 3130, F5, 27) (dual of [3130, 3024, 28]-code), using
(93, 120, 3544940)-Net in Base 5 — Upper bound on s
There is no (93, 120, 3544941)-net in base 5, because
- 1 times m-reduction [i] would yield (93, 119, 3544941)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 150463 600963 913345 723142 327080 062054 726465 853991 068137 954952 105479 773517 716395 570245 > 5119 [i]