Best Known (65−40, 65, s)-Nets in Base 3
(65−40, 65, 32)-Net over F3 — Constructive and digital
Digital (25, 65, 32)-net over F3, using
- t-expansion [i] based on digital (21, 65, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(65−40, 65, 36)-Net over F3 — Digital
Digital (25, 65, 36)-net over F3, using
- net from sequence [i] based on digital (25, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 25 and N(F) ≥ 36, using
(65−40, 65, 115)-Net in Base 3 — Upper bound on s
There is no (25, 65, 116)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(365, 116, S3, 40), but
- the linear programming bound shows that M ≥ 1010 233715 716651 107612 542215 638091 218609 672761 165524 903593 924473 005111 306769 562821 186134 762126 385755 152296 422613 586112 342241 377727 269019 414533 549609 685737 803087 / 94 423144 003278 216048 118473 500831 454684 060079 864523 188758 682434 278034 186489 210172 080884 936271 279930 533580 650501 446289 752944 864745 > 365 [i]