Best Known (12, 68, s)-Nets in Base 7
(12, 68, 20)-Net over F7 — Constructive and digital
Digital (12, 68, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(12, 68, 38)-Net over F7 — Digital
Digital (12, 68, 38)-net over F7, using
- t-expansion [i] based on digital (9, 68, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(12, 68, 142)-Net in Base 7 — Upper bound on s
There is no (12, 68, 143)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(768, 143, S7, 56), but
- the linear programming bound shows that M ≥ 458789 485618 106067 702688 003124 474614 376073 604483 504254 635021 506911 875157 733714 208686 766261 726769 897383 442781 974913 130928 964986 230052 681332 611178 561998 062984 435344 661675 572750 316821 326611 283241 411458 173947 686694 / 149 690095 541387 167002 367382 252335 449710 008937 831541 530469 784063 483096 610550 360446 925819 472709 765255 948214 933185 408075 005226 018717 800265 530033 655595 662765 > 768 [i]