Best Known (72−43, 72, s)-Nets in Base 3
(72−43, 72, 37)-Net over F3 — Constructive and digital
Digital (29, 72, 37)-net over F3, using
- t-expansion [i] based on digital (27, 72, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(72−43, 72, 42)-Net over F3 — Digital
Digital (29, 72, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(72−43, 72, 147)-Net in Base 3 — Upper bound on s
There is no (29, 72, 148)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(372, 148, S3, 43), but
- the linear programming bound shows that M ≥ 140616 689849 151177 540174 469107 623214 902524 373234 563713 296619 681304 722457 754991 147093 951918 153451 548407 544582 982455 263586 804453 976984 329877 768679 866003 344857 085709 968192 295150 158405 086355 117293 815995 399786 105620 103676 565115 407129 402845 238362 530278 975728 254191 863354 567751 991978 849547 640077 469027 501832 766234 432494 073485 807433 390139 517780 408495 / 5 598581 050097 351428 044464 209595 565234 397823 540732 261512 489572 263757 723078 348205 051059 822908 682186 213397 624116 594971 139254 976893 145418 485319 486609 248744 469897 672953 851007 182218 513650 832206 934424 052154 431313 143245 320083 612964 606743 062220 611961 594548 775648 983859 483908 360052 607131 075364 504891 427518 044319 045951 > 372 [i]