MinT - Best Known (46, 46+96, s)-Nets in Base 8

Best Known (46, 46+96, s)-Nets in Base 8

(46, 46+96, 98)-Net over F₈ — Constructive and digital

Digital (46, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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+96, 144)-Net over F₈ — Digital

Digital (46, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 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+96, 1226)-Net in Base 8 — Upper bound on s

There is no (46, 142, 1227)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 174 242928 671597 618387 710446 652241 644229 586119 750788 050978 358663 221199 457712 723773 366179 568363 062603 362790 831082 057084 980866 509756 > 8¹⁴² [i]