Best Known (248−62, 248, s)-Nets in Base 3
(248−62, 248, 328)-Net over F3 — Constructive and digital
Digital (186, 248, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 62, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(248−62, 248, 1016)-Net over F3 — Digital
Digital (186, 248, 1016)-net over F3, using
(248−62, 248, 40705)-Net in Base 3 — Upper bound on s
There is no (186, 248, 40706)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21203 132776 637044 181984 544232 462718 939453 202760 406126 953524 800107 508563 619610 156493 570999 061347 331995 258542 482262 309625 > 3248 [i]