Best Known (26, ∞, s)-Nets in Base 9
(26, ∞, 78)-Net over F9 — Constructive and digital
Digital (26, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (26, 77)-sequence over F9, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
(26, ∞, 110)-Net over F9 — Digital
Digital (26, m, 110)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (26, 109)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 26 and N(F) ≥ 110, using
(26, ∞, 231)-Net in Base 9 — Upper bound on s
There is no (26, m, 232)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (26, 461, 232)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9461, 232, S9, 2, 435), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9418 521061 490606 783376 572129 655376 470042 346977 244166 512430 087580 876100 703271 538599 077428 795109 757867 606368 824176 625862 519535 360805 098340 594128 292067 505140 411336 246312 663198 468679 620624 411471 937703 928948 108179 940461 727836 579940 757514 890462 971499 114249 348204 353035 655056 529616 272774 122660 353689 505858 605630 165220 713948 681705 740067 760422 223854 134244 685007 863995 468266 476141 873108 186845 425195 976742 619006 160852 267698 900719 059240 939851 362535 568253 / 109 > 9461 [i]
- extracting embedded OOA [i] would yield OOA(9461, 232, S9, 2, 435), but