MinT - Best Known (46, 46+76, s)-Nets in Base 8

Best Known (46, 46+76, s)-Nets in Base 8

(46, 46+76, 98)-Net over F₈ — Constructive and digital

Digital (46, 122, 98)-net over F₈, using

t-expansion [i] based on digital (37, 122, 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]

(46, 46+76, 144)-Net over F₈ — Digital

Digital (46, 122, 144)-net over F₈, using

t-expansion [i] based on digital (45, 122, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(46, 46+76, 1678)-Net in Base 8 — Upper bound on s

There is no (46, 122, 1679)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 151 244606 830376 614800 242190 705413 584534 209032 666012 656199 383067 564033 855387 751906 438997 517061 706624 345275 188980 > 8¹²² [i]