MinT - Best Known (148−111, 148, s)-Nets in Base 8

Best Known (148−111, 148, s)-Nets in Base 8

(148−111, 148, 98)-Net over F₈ — Constructive and digital

Digital (37, 148, 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]

(148−111, 148, 121)-Net over F₈ — Digital

Digital (37, 148, 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]

(148−111, 148, 755)-Net in Base 8 — Upper bound on s

There is no (37, 148, 756)-net in base 8, because

1 times m-reduction [i] would yield (37, 147, 756)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 731609 990015 855615 749570 135728 396348 143549 162754 821964 934304 408148 198743 939429 531475 557997 437163 736582 217916 326644 009741 390814 268080 > 8¹⁴⁷ [i]