Best Known (98, 98+33, s)-Nets in Base 5
(98, 98+33, 408)-Net over F5 — Constructive and digital
Digital (98, 131, 408)-net over F5, using
- 5 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+33, 2628)-Net over F5 — Digital
Digital (98, 131, 2628)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5131, 2628, F5, 33) (dual of [2628, 2497, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(5131, 3125, F5, 33) (dual of [3125, 2994, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(5131, 3125, F5, 33) (dual of [3125, 2994, 34]-code), using
(98, 98+33, 812089)-Net in Base 5 — Upper bound on s
There is no (98, 131, 812090)-net in base 5, because
- 1 times m-reduction [i] would yield (98, 130, 812090)-net in base 5, but
- 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]