MinT - Best Known (52, 52+76, s)-Nets in Base 8

Best Known (52, 52+76, s)-Nets in Base 8

(52, 52+76, 98)-Net over F₈ — Constructive and digital

Digital (52, 128, 98)-net over F₈, using

t-expansion [i] based on digital (37, 128, 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]

(52, 52+76, 144)-Net over F₈ — Digital

Digital (52, 128, 144)-net over F₈, using

t-expansion [i] based on digital (45, 128, 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]

(52, 52+76, 2340)-Net in Base 8 — Upper bound on s

There is no (52, 128, 2341)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 790207 105410 149181 578757 984739 164276 339273 368342 633068 892104 982273 267627 197040 070481 467995 784303 414295 905739 725376 > 8¹²⁸ [i]