Best Known (30, 30+42, s)-Nets in Base 3
(30, 30+42, 37)-Net over F3 — Constructive and digital
Digital (30, 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
(30, 30+42, 42)-Net over F3 — Digital
Digital (30, 72, 42)-net over F3, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
(30, 30+42, 165)-Net in Base 3 — Upper bound on s
There is no (30, 72, 166)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(372, 166, S3, 42), but
- the linear programming bound shows that M ≥ 3708 177920 981865 373588 437755 619329 963493 853633 501053 221945 962924 753226 122178 646596 684570 785490 813971 229149 075678 252631 823220 208670 888172 933548 774937 964032 317385 185116 199333 762378 663726 021334 995353 647735 985557 719209 619572 304083 217640 938540 673734 696000 / 156561 852463 373651 529187 845061 951139 819618 179813 617086 729231 310074 778337 668217 120160 348367 793511 265448 893510 422713 110540 923424 266826 849685 171967 550061 800650 508114 845380 137520 223684 048212 787473 386711 548511 501577 011613 > 372 [i]