MinT - Best Known (52, 52+118, s)-Nets in Base 8

Best Known (52, 52+118, s)-Nets in Base 8

(52, 52+118, 98)-Net over F₈ — Constructive and digital

Digital (52, 170, 98)-net over F₈, using

t-expansion [i] based on digital (37, 170, 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+118, 144)-Net over F₈ — Digital

Digital (52, 170, 144)-net over F₈, using

t-expansion [i] based on digital (45, 170, 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+118, 1267)-Net in Base 8 — Upper bound on s

There is no (52, 170, 1268)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3482 477652 077160 211295 685185 156239 244988 329360 181731 076618 394820 092672 077674 773157 437105 063723 986931 649997 886592 061070 640543 376499 075396 294206 372019 293784 > 8¹⁷⁰ [i]