MinT - Best Known (56, 56+108, s)-Nets in Base 8

Best Known (56, 56+108, s)-Nets in Base 8

(56, 56+108, 98)-Net over F₈ — Constructive and digital

Digital (56, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(56, 56+108, 144)-Net over F₈ — Digital

Digital (56, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(56, 56+108, 1622)-Net in Base 8 — Upper bound on s

There is no (56, 164, 1623)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13044 209970 586171 250136 451887 718223 883031 301813 503256 476748 676423 246129 176827 831017 246737 612358 809553 064186 071943 240834 665648 472323 506387 331283 889074 > 8¹⁶⁴ [i]