Best Known (150−113, 150, s)-Nets in Base 8
(150−113, 150, 98)-Net over F8 — Constructive and digital
Digital (37, 150, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(150−113, 150, 121)-Net over F8 — Digital
Digital (37, 150, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(150−113, 150, 749)-Net in Base 8 — Upper bound on s
There is no (37, 150, 750)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 149, 750)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 386 381319 763095 504436 887291 250139 980773 616862 414357 996131 363213 127832 038426 731082 207060 169959 418023 670108 589649 165696 930237 761752 098356 > 8149 [i]