MinT - Best Known (126−89, 126, s)-Nets in Base 8

Best Known (126−89, 126, s)-Nets in Base 8

(126−89, 126, 98)-Net over F₈ — Constructive and digital

Digital (37, 126, 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]

(126−89, 126, 121)-Net over F₈ — Digital

Digital (37, 126, 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]

(126−89, 126, 879)-Net in Base 8 — Upper bound on s

There is no (37, 126, 880)-net in base 8, because

1 times m-reduction [i] would yield (37, 125, 880)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 80463 225517 266722 317593 358979 049278 962610 425632 534293 189077 024758 863126 801726 881260 983901 189011 629887 994617 056601 > 8¹²⁵ [i]