MinT - Best Known (37, 37+67, s)-Nets in Base 8

Best Known (37, 37+67, s)-Nets in Base 8

(37, 37+67, 98)-Net over F₈ — Constructive and digital

Digital (37, 104, 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]

(37, 37+67, 121)-Net over F₈ — Digital

Digital (37, 104, 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]

(37, 37+67, 1218)-Net in Base 8 — Upper bound on s

There is no (37, 104, 1219)-net in base 8, because

1 times m-reduction [i] would yield (37, 103, 1219)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1066 459470 376557 412647 492521 870135 381778 678641 583371 199029 955065 596570 540747 138024 186680 791020 > 8¹⁰³ [i]