Best Known (25, 25+∞, s)-Nets in Base 9
(25, 25+∞, 78)-Net over F9 — Constructive and digital
Digital (25, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (25, 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
(25, 25+∞, 96)-Net over F9 — Digital
Digital (25, m, 96)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (25, 95)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 25 and N(F) ≥ 96, using
(25, 25+∞, 223)-Net in Base 9 — Upper bound on s
There is no (25, m, 224)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (25, 445, 224)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9445, 224, S9, 2, 420), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20 722162 714195 481493 126091 989290 988093 607872 112463 814922 137011 295134 522690 280031 866797 278934 989678 319714 955166 490575 102715 872105 084801 338686 048404 473855 313189 282760 450588 742465 159318 452746 351997 315284 271849 493863 318901 961331 970708 091238 567857 105590 831094 435973 837888 639551 372509 476050 265192 830744 400206 537719 461173 487676 108317 120618 322461 404326 981656 708039 923466 088854 975599 807610 958943 110185 244202 669018 556739 042892 758202 219173 / 421 > 9445 [i]
- extracting embedded OOA [i] would yield OOA(9445, 224, S9, 2, 420), but