Best Known (64, 95, s)-Nets in Base 5
(64, 95, 252)-Net over F5 — Constructive and digital
Digital (64, 95, 252)-net over F5, using
- 13 times m-reduction [i] based on digital (64, 108, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 54, 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, 54, 126)-net over F25, using
(64, 95, 519)-Net over F5 — Digital
Digital (64, 95, 519)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 519, F5, 31) (dual of [519, 424, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- discarding factors / shortening the dual code based on linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using
(64, 95, 38529)-Net in Base 5 — Upper bound on s
There is no (64, 95, 38530)-net in base 5, because
- 1 times m-reduction [i] would yield (64, 94, 38530)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 504896 662682 416567 363427 563885 011567 175645 092111 009346 904768 423465 > 594 [i]