Best Known (118−28, 118, s)-Nets in Base 5
(118−28, 118, 408)-Net over F5 — Constructive and digital
Digital (90, 118, 408)-net over F5, using
- 2 times m-reduction [i] based on digital (90, 120, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 60, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 60, 204)-net over F25, using
(118−28, 118, 3261)-Net over F5 — Digital
Digital (90, 118, 3261)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5118, 3261, F5, 28) (dual of [3261, 3143, 29]-code), using
- 119 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 6 times 0, 1, 14 times 0, 1, 31 times 0, 1, 62 times 0) [i] based on linear OA(5112, 3136, F5, 28) (dual of [3136, 3024, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(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(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 119 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 6 times 0, 1, 14 times 0, 1, 31 times 0, 1, 62 times 0) [i] based on linear OA(5112, 3136, F5, 28) (dual of [3136, 3024, 29]-code), using
(118−28, 118, 1176827)-Net in Base 5 — Upper bound on s
There is no (90, 118, 1176828)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 30092 972777 126069 994737 435305 850289 782895 254562 303192 072911 774003 481225 284422 889025 > 5118 [i]