Best Known (100−25, 100, s)-Nets in Base 5
(100−25, 100, 400)-Net over F5 — Constructive and digital
Digital (75, 100, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 50, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(100−25, 100, 2388)-Net over F5 — Digital
Digital (75, 100, 2388)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5100, 2388, F5, 25) (dual of [2388, 2288, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
(100−25, 100, 772323)-Net in Base 5 — Upper bound on s
There is no (75, 100, 772324)-net in base 5, because
- 1 times m-reduction [i] would yield (75, 99, 772324)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1577 737170 330664 085204 653821 241329 104350 874133 915900 735315 975371 363073 > 599 [i]