MinT - Best Known (149−112, 149, s)-Nets in Base 8

Best Known (149−112, 149, s)-Nets in Base 8

(149−112, 149, 98)-Net over F₈ — Constructive and digital

Digital (37, 149, 98)-net over F₈, using

net from sequence [i] based on digital (37, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(149−112, 149, 121)-Net over F₈ — Digital

Digital (37, 149, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(149−112, 149, 749)-Net in Base 8 — Upper bound on s

There is no (37, 149, 750)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 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]