Best Known (75−52, 75, s)-Nets in Base 4
(75−52, 75, 34)-Net over F4 — Constructive and digital
Digital (23, 75, 34)-net over F4, using
- t-expansion [i] based on digital (21, 75, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(75−52, 75, 45)-Net over F4 — Digital
Digital (23, 75, 45)-net over F4, using
- net from sequence [i] based on digital (23, 44)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 23 and N(F) ≥ 45, using
(75−52, 75, 143)-Net in Base 4 — Upper bound on s
There is no (23, 75, 144)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(475, 144, S4, 52), but
- the linear programming bound shows that M ≥ 2125 414354 070862 854900 643624 159873 812749 383623 575655 419708 768093 274583 720527 789958 647139 573116 212747 908130 287913 609396 134546 112211 579367 966814 012953 623245 004862 302580 682149 248702 218174 975510 279492 291821 927335 829850 187019 593627 703822 107622 450543 139723 769132 341633 330241 379221 110784 / 1 437482 861328 887545 000336 259054 641559 061865 445846 776951 781520 734058 843536 163059 022978 766750 993310 069169 815109 331218 021787 193359 989829 263376 124499 439521 845834 376957 885716 329405 444388 195937 869981 286060 442586 771388 042783 236131 713143 660675 > 475 [i]