MinT - Best Known (46, 46+63, s)-Nets in Base 8

Best Known (46, 46+63, s)-Nets in Base 8

(46, 46+63, 98)-Net over F₈ — Constructive and digital

Digital (46, 109, 98)-net over F₈, using

t-expansion [i] based on digital (37, 109, 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+63, 144)-Net over F₈ — Digital

Digital (46, 109, 144)-net over F₈, using

t-expansion [i] based on digital (45, 109, 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+63, 2464)-Net in Base 8 — Upper bound on s

There is no (46, 109, 2465)-net in base 8, because

1 times m-reduction [i] would yield (46, 108, 2465)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 34 260004 448539 332613 210574 459659 376269 820650 066447 632167 446443 137466 690917 283487 011167 762972 744928 > 8¹⁰⁸ [i]