Best Known (26, 68, s)-Nets in Base 3
(26, 68, 36)-Net over F3 — Constructive and digital
Digital (26, 68, 36)-net over F3, using
- net from sequence [i] based on digital (26, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using
(26, 68, 37)-Net over F3 — Digital
Digital (26, 68, 37)-net over F3, using
- net from sequence [i] based on digital (26, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 25, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 25 and N(F) ≥ 36, using algebraic function fields over ℤ3 by Niederreiter/Xing [i]
(26, 68, 116)-Net in Base 3 — Upper bound on s
There is no (26, 68, 117)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(368, 117, S3, 42), but
- the linear programming bound shows that M ≥ 117688 677034 371150 621267 441012 191945 699509 786586 414202 785608 822882 266942 917131 914689 407902 641112 044580 185151 160708 720843 820397 646660 433506 256247 / 388 484897 528912 368351 403561 573056 452570 889875 851861 940521 311969 565349 433313 959589 947946 383067 599375 798269 567950 > 368 [i]