Best Known (43, 43+∞, s)-Nets in Base 7
(43, 43+∞, 44)-Net over F7 — Constructive and digital
Digital (43, m, 44)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 43)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 43)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 43)-sequence over F49, using
(43, 43+∞, 105)-Net over F7 — Digital
Digital (43, m, 105)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
(43, 43+∞, 278)-Net in Base 7 — Upper bound on s
There is no (43, m, 279)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (43, 833, 279)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7833, 279, S7, 3, 790), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11576 501833 335269 393886 152382 170043 096417 165257 162890 113309 963375 767017 500187 234257 826449 529440 927913 055894 203541 656878 241219 153910 644372 678097 937423 695542 080148 084251 588780 817244 601577 367852 501343 531799 185314 901498 808683 184436 849833 741627 345924 145613 024139 210068 376610 632120 348303 542065 093476 451917 777512 161422 126694 715620 372756 894143 344680 430333 312106 826037 182038 227027 413421 209699 811522 413261 181185 500583 372448 263779 563117 155109 638919 026626 242745 143935 100587 901864 216728 538683 921247 770801 317063 974240 139359 714800 090625 822238 195371 365474 949670 988741 476261 770620 022093 101625 207866 488365 363245 742695 469993 175131 121889 103932 128218 556718 011278 848018 101563 458309 852992 118947 186910 684782 349822 852101 077556 800875 / 113 > 7833 [i]
- extracting embedded OOA [i] would yield OOA(7833, 279, S7, 3, 790), but