Best Known (98, 98+32, s)-Nets in Base 5
(98, 98+32, 408)-Net over F5 — Constructive and digital
Digital (98, 130, 408)-net over F5, using
- 6 times m-reduction [i] based on digital (98, 136, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 68, 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, 68, 204)-net over F25, using
(98, 98+32, 3029)-Net over F5 — Digital
Digital (98, 130, 3029)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5130, 3029, F5, 32) (dual of [3029, 2899, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(5130, 3144, F5, 32) (dual of [3144, 3014, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [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(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(54, 19, F5, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,5)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(5130, 3144, F5, 32) (dual of [3144, 3014, 33]-code), using
(98, 98+32, 812089)-Net in Base 5 — Upper bound on s
There is no (98, 130, 812090)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 7 346919 300108 082933 750506 035971 754602 799404 259568 107037 382796 463424 803072 511161 362094 105345 > 5130 [i]